I know that the pressure increases in a tire when it warms up to operating temperature, but is there any size expansion? The increase in pressure would say no, but I wondered anyway.  

a tire stays the same size no matter the pressure, their construction doesn't allow the "size" to increase. it will affect the hight of the vehicle slightly and the contact patch if its deflated some but the overall dimensions stay the same

Actually it was the height I was wondering about. It seems that when I look at a cold tire it does appear a little underinflated and flatter on the ground, which would make sense as tire pressure should be checked hot.

Any idea how much is "slightly?"

assuming your tires are 100% flexible, heres how it would work.

lets say the tire carries 500 lbs when the tire is at 50 psi the contact patch would be 500/50 = 10 square inches.

at 25 psi the tire would need a contact patch of 500/25 = 20 square inches.

to make the bigger contact patch the tire isn't as tall.

of course tires arent that flexible, sidewalls suport some tread construction also messes up those calculation, but its a basic view of whats going on.

as tires heat up pressure goes up, so the contact patch shrinks and the height increases its usualy not much, but it can be.
I remember on warm spring day I noticed my car tire was bulging lik it shouldn't, I checked the pressure and it was 90psi! I used a pencil to let the air out of the valve, the first 4" got coated in frost