The Apple IIgs can have the usual seven cards an Apple II can have plus RAM which has an additional slot. Other devices can end up inside the IIgs such as an adapter for the Game I/O socket or the Ensoniq I/O expansion connector. How many cards can safely be put in a IIgs? I have a ROM 03 IIgs with the original power supply so heat could be a problem.
In general, the IIgs was designed to have a full house in regards to expansion cards, just like every other member of the expansion slot Apple II family. There are guidelines for how much power a card can draw. However, there are not guidelines how how much heat a card can produce. Despite this, I'm not aware of any expansion cards from the era that produced excessive heat as the voltage and draw was much lower in those days; the "cook your eggs" measurements we see today with CPUs / GPUs more or less didn't really exist back then. I want to say that I've read in the past that the maximum draw per-card is around 300-500ma which doesn't translate to a heck of a lot of heat, but then again I'm not an expert on that topic.
That being said, it was always considered a good idea to put a fan on the system and many people opted for the Kensington System Savers that had a small fan to draw air through the machine. When I ran a BBS back in the day with 7 cards and a RocketChip in my //e, I would never describe the temperature of the air coming out of the KSS fan as more than "slightly warm". However, it was understood that having a fan would increase the life of the components in the machine.
Ultimately it seems that you're concerned about your power supply. The PSU in a IIgs was all you needed and I don't recall seeing aftermarket upgrades for higher wattage units like we do today. We simply don't have the same wattage .. err.. "arms race" with the 8-bit kit from the 80s. But if you are concerned about your PSU, there are two things you could do:
- Get a new PSU or refurbish it (i.e. inspect, re-cap, re-solder, etc.).
- Get a Kensington Saver GS or some other fan for the unit.
Doing #1 will probably be the best route since you're guaranteeing the machine will not have power problems for at least a decade. While you're at it, make sure the battery is fresh (I think they were removable in the ROM 03) since that is the more likely cause of IIgs death!
UPDATE 2016-09-20: Slight update. I stated that I didn't recall aftermarket PSUs for the II, but come to think of it there was the Vulcan hard disk from Applied Engineering which was effectively a replacement 70 watt PSU with hard drive built in (and accompanying controller card). If anything is going to be a draw on an Apple II besides the disk drives (which could only run one at a time anyway), a spinning HDD would be it and I'm assuming the Vulcan covered the bases.