First, the word “cold” means “at the ambient temperature” (outside temperature) and not heated due to operation. Ergo, any tire that has been operated has built up a little heat (or a lot), so the pressure reading is elevated - and you can’t tell how much unless you take the tire’s temperature.
Second, as the outside temperature increases, so does the pressure - about 1 psi for every 10°F. It is common for folks to recommend that tire pressures be taken in the morning so the tire is “cold” (un-operated). The fact that the outside temperature rises during the day complicates matters, but we are usually talking about a 20°F rise, so that’s only 2 psi! Not enough to worry about.
What is of concern is if the tire’s pressure was adjusted when the outside temperature was 80°F, and the weather changes to 30°F - a 50°F drop (5 psi)
What is also not usually known is that new tires will grow. It takes about 24 hours for most of the growth to take place - and that affects the size of the air chamber - about 2 psi worth. So if you are in the retail tire trade, it isn’t a bad idea to set the presure 3 to 5 psi high to account for all those factors. However, used tires - particularly tires already inflated - have already experienced this growth, so no adjustment for growth is needed.
And just to reiterate a point, the vehicle tire placard will list the original tire size and the proper pressure for that size. If the tire in question is the same size as what is listed on the vehicle tire placard, then the pressure listed there is appropriate. However, if a different tire size is used, then the pressure has to be recalculated. That requires the use of tire load tables, which are difficult to find on the internet because they are subject to copyright laws. However, I have them and would be happy to do the calculation.