On August 2nd, 2010 I walked through Regent's Park with my digital thermometer. These are the results plotted on a map. Further below is the analysis. My walks fit part of the scientific theory but there are some deviations.
Fun and discovery
Maybe I have a strange idea of what “fun“ is, but doing the walk, recording the measurements, making the map and seeing what I can learn from it feel like a “voyage of discovery“. I'm always looking for ways of revealing the “invisible city“ and this walk is another way of showing invisible effects, that would otherwise remain hidden. Also, it is wonderful to see that even such a simple concept like “temperature“ behaves in an amazingly complex manner.
Analysis and surprising complexity
According to Marcel Minnaert the temperature difference between the park and the built-up area should not be that big. But it fits with my measurements of a difference of “a few degrees“.
77. The temperature in the woods
The delicious fresness that we feel in the woods on a hot day makes us suspect that a significant temperature difference with the outside air will be found. But behold! The thermometer inside the beech wood and outside of it, in the shade, shows, even on a warm summer afternoon, a temperature difference of only one degree or a few degrees! [...] In a pine forest, the difference is even less clear. [...] The peculiarities of temperature, humidity, wind speed in town or in the forest, clearly distinguished from those in the rest of the area, are best expressed by speaking of "the local climate" that prevails in these different areas. 
Some modern measurements - found in a quick search on Google - also seem to fit my own measurements. The differences are indeed small beyond the park boundary. The temperature differences I measured seem to be too big compared with the literature.
Urban open spaces such as parks can act as urban cool islands. For example, in Seoul, Korea, the many Lee Dynasty royal palaces and tombs act as urban cool islands that reduce the temperature of the park compared with the surrounding urban areas. [...] Results of the investigation show that the average air temperature differences due to the park in the nearby subway station was 1.76°C. [...] The air temperature-reducing effect due to the park decreases rapidly from the park boundary, because of the urban morphology and land use. 
However some articles show that the temperature differences can be big indeed. But the London parks are - very visibly - not irrigated, the grass was burnt and yellow, almost desert-like.
In Vancouver, parks are typically 1-2 C, but in ideal conditions can be almost 5 C cooler than their surroundings. Larger PCI (park cool islands) are possible in Sacramento where irrigated greenspace can be 5-7 C cooler. Park type, especially the extent of irrigation and the presence of trees, is important in PCI development. During the day trees may play an important role in establishing a cool park effect, perhaps through a combination of shade and evaporative cooling. At night it appears that the surface geometry and moisture status of the park are important controls on surface cooling. Open parks (with higher sky view factors) that have dry soils (and hence lower thermal admittance) cool the most. Nocturnal cooling in open grass parks is often similar to that at rural sites. The influence of parks on air temperatures appears to be restricted to a distance of about one park width. 
But the temperature differences behave in a more complex way than one would expect. Now I see that I also should have looked at the wind direction and wind speed.
Large green areas have a cooling influence on their surrounding built-up area, thus reducing the stress produced by the heat island. Traverses made on clear nights with light wind show that Chapultepec Park (500 ha) in Mexico City is 2–3 °C cooler with respect to its boundaries and its influence reaches a distance about the same as its width (2 km).
[...] For a recent period of four years, mean monthly minimum temperature differences between a climatological station located in the park and the Tacubaya Observatory (- 700 m south of its southern limits) reach 4.0 °C at the end of the dry season in April, whereas during the wet months they are only 1 °C cooler (in July). On sunny mornings the park heats up more slowly than the built-up section at Tacubaya; but two hours after midday there is no significant difference in temperature as shown by mean maximum temperatures. At this time, the canopy layer is well mixed and Tacubaya being downwind (from N or NE) is then under the cooling influence of the park.
But east and north of the park toward the densely built-up area (where the heat island is located), mean maximum temperatures at the park station are 2–3 °C cooler. 
But even inside parks there can be significant differences in temperature, changing between different times of day and night. But I didn't notice large differences in the parks.
This study underlines the differences in summer human wellbeing in an urban park between a grass area and a forested one: during the day the forested area is meanly 3 °C cooler than the grass area, but during the night the grassland is cooler than the woodland of almost the same amount. [...] As the cooling effect of green areas is both during the day (in the wooded area) and during the night (in the grassland area), and as the lower temperatures during the night seems to have very important consequences in human health, this study wants to suggest that both grassland and woodland areas of a park can have different positive effects on human wellbeing during all the hours of the day. 
Some more research about the complex temperature (and humidity) behaviour inside of urban parks. In a city always look for parks with high trees!
The research was conducted in three different types of urban parks: a park with grass and a few low trees, a park with medium sized trees and a park with high and wide-canopied trees. The results showed that an urban park that contains high trees with a wide canopy has the maximum cooling effect during daytime, reduces temperatures by up to 3.5 °C and lowers heat stress values despite increasing relative humidity values. An urban park that contains dense, medium sized trees can also reduce temperatures during daytime by up to 2.5 °C as well as slightly lower heat stress. However, during nighttime it can create uncomfortable climatic conditions owing to the reduction of wind velocity and increase in relative humidity. An urban park covered with grass can be warmer and sometimes even more humid than the built-up area during the day, which increases heat stress values. 
 Marcel Minnaert, De natuurkunde van 't vrije veld. Deel II. Geluid, warmte, elektriciteit. W.J. Thieme, Zutphen 1939
 Effect of an urban park on air temperature differences in a central business district area
Sang-Hwa Lee, Kyoo-Seock Lee, Wen-Cheng Jin and Ho-Kyung Song, Landscape and Ecological Engineering Volume 5, Number 2, 183-191
 The thermal regime of urban parks in two cities with different summer climates, R. A. Spronken-Smith; T. R. Oke, International Journal of Remote Sensing, Volume 19, Issue 11 July 1998 , pages 2085 - 2104
 Effects of vegetation on urban and buildings climate, Influence of a large urban park on temperature and convective precipitation in a tropical city, E. Jaureguia, Energy and Buildings, Volume 15, Issues 3-4, 1990-1991, Pages 457-463
 AIR TEMPERATURE DISTRIBUTION IN AN URBAN PARK: DIFFERENCES BETWEEN OPEN-FIELD AND BELOW A CANOPY, Martina Petralli, Luciano Massetti and Simone Orlandini, The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan
 Climatic behavior of various urban parks during hot and humid summer in the mediterranean city of Tel Aviv, Israel, Oded Potchter, Pninit Cohen, Arieh Bitan, International Journal of Climatology, Volume 26, Issue 12, pages 1695–1711, October 2006
 How Cities Use Parks for ... Climate Change Management