It was always drummed into me that you should check tyre pressures when the tyre was cold, because as Dodger was told us the pressure in the tyre will increase with temperature. As Thingy points out, the temperature of the tyre is affected by a range of factors, but probably the most significant is the friction heating caused by the flexing of the tyres side walls when rolling.
As Damian points out, the tyre manufactures are well aware of this characteristic, and will build into there tyres an allowance to cover the normal increase in running and environmental temperatures.
In a normal road vehicle, the majority of heat generation come from the flexing of the sidexwall when rolling, if a tyre is overloaded or is running underinflated, the side walls will deflect more, this will generate more heat and that combination of physical movement and temperature will do more damage to the tyre wall compound, potentially leading to premature failure.
There have been many debates on the forum about selecting the correct tyre pressures with some quoting values to a hundredth of a Bar. But the reality is it's very very unlikely any consumer has access to a pressure guage that can accurately read a tyre pressure to that precision. It's most likely that none of our gauges can do better than +/- 0.1 Bar. Consequently there will be a modest variation in real inflation pressures depending on the gauge used.
Given that pressure accuracy can't be guaranteed, and the fact that the pressure will vary with temperature, how accurate can we be expected to be? My guess is that allowing for the inherent variations between gauges, a measurement with a tolerance of +/-0.2 Bar (approx +/- 2psi) is about as good as we can get.
What is arguably more importantl is that all the tyres on a vehicle should be checked by the same gauge, to create a consistency of measurement.