But if the discharge current approaches the maximum designed load of the UPS, then the unit would become hotter and hotter with time. It's not a problem with a battery that'll only run for two minutes at maximum load (like most cheap UPSes), but it may be a problem with a car battery.
If semiconductors get too hot, they did so, destructively, in the first minute. Semiconductors and other electronics inside the regulator/inverter do not get any hotter an hour later.
Electronics are designed for maximum load. Electronics will be at worst temperatures in the first ten seconds - often sooner. After a minute, or after an hour, those electronics will be at the same temperature. If one hour will harm electronics, then so does the first minute.
Furthermore, electronics are designed to be at ideal temperatures even when the room temperature rises to above 100 degrees F. UPS electronics in a 70 degree room means the electronics will be another 15 degrees C cooler.
Enlarging a battery will do nothing to create more heat (in battery or in electronics) despite Mfenn's post #17 that speculates otherwise.
Whereas Gilford's idea works in theory, it makes no sense once we add numbers and experience from hardware design. If electronics was going to become too hot, it did so in the first minute in a 100 degree F room. Even in a 100 degree room, electronics remain well below destructive temperatures. A destructive junction temperature of hundreds of degrees inside a semiconductor is achieved in seconds. Will not get any hotter an hour later.
RebateMonger - your open case with larger batteries means everything works at the same or, more likely, lower temperatures. Larger capacity battery will create less heat when charging and discharging. Open case means increased ventilation and lower temperatures. Larger capacity battery will never increase stress on electronics (as long as the battery is same technology). Consumer electronics are also designed to work perfectly ideal even when a room temperature increases another 20 degrees C. Just another reason why a UPS in a 70 degree F room is perfectly fine.
So many numbers all say posted fears come only from wild speculation. Are not tempered by design experience. Your modifications imply everything is operating at an even lower temperature. Exposed is speculation by ignoring technical knowledge, design experience, and numbers. Numbers such as a lower battery temperature due to a lower series equivalent resistance and due to larger surface area. Larger battery (of same technology) does not increase stress on electronics.