You have a gas leak somewhere under your hood.(if it had carbs or was flooding, it would also smell) But that year and type of car has only one way to really get fuel out of the system and into the vent system - backfiring through the MAF or being so flooded it won't normally run or start - same difference - gas vapors back up past the MAF and into the engine compartment. This is unlikely, but it has happened to me once years ago - though it made a loud noise and was completely obvious.
Another option is that you are dumping huge amounts of gas into your antifreeze through a bad gasket or seal, though this is farily unlikely as your car wouldn't really be running hardly at all with such a huge problem. Unless your heater core was also leaking, you'd never smell the antifreeze or gas anyways, as the air flow over the heather core is just air.
So what's happening?
My father's 96 Park Avenue almost caught fire this way - one of the fuel hoses had a leak and was dumping gas out of it onto the engine block(!!!!) And it was getting 12-15mpg for the two days that it was doing it before he figured it out. By some miracle it didn't catch fire. note - the mechanic was also incredulous at his stupid luck.
It smells because the vapors are much more noticeable when they are hot - but it's still leaking through the little holes in the firewall and ventilation system - just probably not enough for you to easily smell it with the AC on.
Gasoline is one of the smells that is a huge "do not drive" signal.