For the record, I almost always order larger batteries than what came with the UPS originally. So if my UPS originally came with 12V 7.4Ah cells, I certainly would replace them with 12V 9Ah cells.
The most important thing is to ensure the voltage is the same. Next, make sure the terminals are the same size. See
F1 vs F2 terminal connector size. There are simple adapters but the battery compartments in most UPS leave little to no room for adapters. So best to ensure you get the right size from the start. And as newtekie1 noted, the physical size of the battery itself matters too. Most are "about" the same size.
As far as the charging circuit getting hotter - that "should"
not happen. And even if it does, it will only be for a short time until the cells take on enough charge from a nearly discharged status. And in any case, the charging circuits "should"
never "over" heat because even cheap UPS have thermal and excessive current protection features built in. This is because it is not uncommon for SLA batteries to develop internal shorts when they fail. Such shorts would result in excessive current demands on those charging circuits.
This is why you can put a tiny "trickle" charger on a big car battery (which use the same "sealed lead-acid" technologies as UPS batteries) and not burn up the charger.
I did say "should" not and "should" never because I am assuming the UPS and cells are in proper working condition.
That's because it is. In other applications, the larger Ah rating could support larger loads. In the case of a UPS, you get longer battery run times. That's a good thing.