The descriptions of urban warming dwell on the heating of the air by the local infrastructure. There is more to it than simple conduction to the air mass from warmed surfaces.
In the far infrared, where the peak radiation wavelength is determined by the temperature, much of the energy from warmed surfaces is absorbed by the greenhouse gases in the atmosphere within a meter or so. These gases then re-radiate to any other nearby surfaces or gases further away and conduct by collisions with other air molecules to heat the air. There are also windows in the infrared spectrum that let warm surfaces radiate directly to other surfaces. Thus for a temperature measuring instrument, the temperature measured is a combination of the air temperature conducted to the thermometer by air flowing past it and IR heating from nearby surfaces. This is why in the polar regions when measuring very low temperatures, a person approaching the thermometer will raise the temperature reading.
This second source of increased temperature causes “urban warming” even where the location is strictly rural. A measuring station at an isolated research station or farm can have “urban warming” when the thermometer is in close proximity to just one heated building.
Figure 1 is a visible and FLIR IR image of the MMTS station at the Perry, Oklahoma Volunteer Fire Department. The image is from an article by Anthony Watts here, used by permission.
Painting the MMTS white only reduces direct heating by sunlight at visible wavelengths. In the long wavelength IR, any paint, black, white, or any other color, has the same emissivity, more than 0.9, and will absorb IR equally well. In Figure 1, the west-facing uninsulated door is very warm compared to the north-facing wall. It is being heated both by the sun and the building interior. The MMTS is slightly warmer (perhaps 2 or 3 degrees) than the mounting pipe. The pipe is unpainted, somewhat shiny, with a lower emissivity, reflecting more of the IR. Thus it appears black, where the MMTS is a warmer dark purple.
Pierre has posted on a German study of the temperature shifts with the installation of electronic thermometers here. This shift is due to the different way a glass thermometer in a wooden shelter responds to IR in the vicinity and the way a compact modern MMTS responds. There is also the issue of the need for cabling that leads to a distance bias to the nearest building.
Every weather station should be checked for IR emissions in the “view-shed”, the surrounding surfaces and buildings. This should be done at several hours of the day, to catch sunlight warming all the surfaces, and internal building heating variations.