To some degree you are right, black surfaces cool faster at night. It’s not safe to assume the effect is symmetrical, though, because the incoming radiation is shortwave visible light, while the outgoing is longwave IR light (and while black surfaces tend to be darker at all wavelengths, that’s not necessarily so) and because the rate of heat flow depends on the temperature of the surroundings too, which are not necessarily symmetrically hotter/colder than the ground between day and night. If the warm body is mainly radiating towards surroundings that are also warm (because it is surrounded by tall buildings) then the heat loss will be slowed, but as the heating during the day is dominated by input from a single direction, the heating is not symmetrically reduced by the buildings.

Yes, that’s a fair summary. The energy flow in is also a little bit higher (for the same sort of reason a black surface left out in the sun gets hotter than a white or silver one), but the main reason for the effect is the energy flow out being smaller for a given temperature.

Part of the effect is due to increased absorption. While the incoming sunlight is the same, black tarmac and roofing absorbs a lot more of it than green grass or tree canopies. There is also the “canyon effect”, in which light reflects off high buildings giving it several chances to be absorbed, as opposed to flat ground where once it reflects it’s unlikely to hit anything else.

There are also changes to the rate at which it is lost. Plants and moist soil lose a lot of heat by evaporation – water takes a lot of energy to turn it into vapour. Plants are especially effective, as they use this one-way water flow as their circulation system. If water is locked under concrete or drained away rapidly, you soon get a far more arid surface than in nature. There are also significant changes in micro-convection and the effect of wind. Heat is normally conducted only into the first few centimetres of air, but air micro-currents rapidly carry that away and replace it, speeding the process enormously. When nearby surfaces are at different temperatures you get convection. Urban surfaces tend to be more uniform on the micro-scale, and tall buildings shelter you from the wind on a larger scale. And grass and trees are flexible enough to move in the wind, which further enhances cooling efficiency.

There are also more complicated processes involving the air well above ground level, such as inversion layers in the first few hundred metres, and different effects depending on whether it is cloudy, windy, or has recently rained. The air temperature changes rapidly with altitude near the surface, so you have to be careful to define exactly what is meant by “the surface air temperature”. The trend at two metres may not be the same as the trend at ten metres or ten centimetres.

Direct heat energy from mankind is not usually significant, unless your thermometer is very close to the source. Putting thermometers next to air conditioning units and at sewage treatment plants could well cause such influences.

Generally, the temperature difference between country and city is some fraction of a degree C during the day and several degrees C at night, both upwards. And because the temperature stations that go back a century or more were probably not in such urbanised environments originally, so one would expect there to be a rising bias to the temperature measurements.

However, it is worth pointing out that much of the countryside has experienced land use changes too, from modern farming methods and the spread of agriculture for example. Corn instead of trees will affect the sunlight absorbed. Irrigation will affect evaporation. Big open fields instead of scrub or forest will affect convection and wind. These may affect rural temperatures systematically too. (And if there are systematic climatological changes in precipitation or windiness, or ecological changes due to the wildlife changing character these may affect natural surface temperatures independently of radiative heat balance. That’s not related to UHI, though, and shouldn’t be corrected for.)

Despite this expectation of a warming effect, some of the climatologists have reported contrary results. Hansen has applied UHI corrections to data in which over 40% increase urban temperatures relative to the surrounding countryside, indicating that he has found measurements taken in cities are often cooler than they should be. Parker compared temperature trends on windy and non-windy nights (although there is dispute over whether his chosen threshold was appropriate) and found no difference, showing that there is no significant UHI trend.

That urban heat islands exist is easily measurable (as in the above linked science project), and there has undoubtedly been a trend in urbanisation around many weather stations over the past century. How these can both be true, and yet no systematic trend in UHI result is a bit of a mystery.