I've heard, but never confirmed, that on warm days ATC will not put
any IFR traffic in the flight levels lower than about 20,000' to avoid
potential errors of this nature.

FAR 91.121(b), Lowest Usable Flight Levels are predicated on Altimeter
Settings, not temperature, but yes, high temperatures are associated with
abnormally high pressure.


This is also the reason that higher altitude airports tend to have
higher altimeter settings. The altimeter setting is obtained by
getting the altimeter to read the airport's true altitude and that
will require a higher altimeter setting for higher altitude airports
on warm days.


Altimeter settings are "adjusted to Sea Level", the altimeter is referenced
to sea level. True.
Altimeter settings to read the airports true altitude for warm days will be
higher than for colder days. Warm days are associated with High Pressure
weather patterns.

Yes, a set volume (column) of air, at standard sea level pressure will have
equal pressure readings at sea level and at a set "physical true" altitude
or elevation above sea level. Chill the column significantly and the
physical true altitude for the same pressure reading will be lower, raise
the temperature, and the column will expand and read a higher true altitude
for the same pressure altitude.

BT