Radiator caps only cause a boil over under load. at idle they won't.

FYI on the fans, most cars are wired so the fans come on when the A/C is on, so your fans could still not be coming on due to engine temp even if they do come on with the a/c.

Can you hear the engine fan from inside the car? On many cars it is loud enough that at low speeds/stop it is audible if the windows are open.

Next time it starts getting hot, listen for the fan. If you can't hear it, turn the a/c on, but set it to the hottest setting with the blower at zero. This will limit the strain the a/c adds to the car, while kicking on the fans. If you hear the fans kick on and the temp drops either the temp sensor for the fans, the fan relay or the fan controller are borked.

As many are suggesting, current signs point to it being something related to the fans. I wanted to direct-wire the fan last night (preferably with a switch), but then I found out we had plans, and I didn't have time to do it this morning.

I don't understand have the A/C on but the blower on zero. If I turn the blower off, the A/C turns off. I can turn the A/C on and the blower on 1...

However, if it is just the fans causing the problem, and the A/C turns them on, shouldn't I be able to run the A/C at any setting? I the car never used to overheat, even with very hot outside air and heavy A/C use.

EDIT: Also, when it is very hot out, I often hear the fans of other cars running after the car has been turned off. My car has *never* done that while I owned it (which is only since spring this year). That strikes me as odd.

If after testing the fans you still have the problem you could replace both the radiator cap and the thermostat for about $10-$15 and depending on how hard the thermostat housing is to get to probably well under an hour of your time. Personally I like to change them every few years anyway as preventive maintenance and more peace of mind. That is still no guarantee I won't have a problem, but I figure it helps. I have the cooling fan on my '88 Escort straight wired to a toggle switch, because it wasn't cycling the way it should. I only have to use it when I am in town doing lots of stop and go driving.

Yes, sorry I failed to think that though. What I meant was to keep it low so the system doesn't possibly pull heat from the heater core and skew the results.

The cooling system may be marginal, and the fan problem is pushing it over the limit. I'd make sure the fans are working and/or repair them, then give the rest of the system a going over.
Have you checked the waterpump for play? Assuming it is belt driven (I don't know those motors at all) all you need to do is grab the pulley bolted to it and wiggle it, any play at all, even the tiniest amount means the pump is worn and needs replacing.

That isn't proof of a problem, some cars are wired for the fan to be able to come on that way, some aren't. I don't know how yours is wired.

Ok, here's an update for those that were chiming in on this:

After one weekend of not having time or the proper tools to work on this, plus not really believing it was the thermostat, I decided I needed to take it to a shop. I got a recommendation for a really good, honest, inexpensive shop from someone, and once I called to make an appointment, I believed them: A one week wait to get the car in the door.

They saw the car last Friday, and the guy thought it was probably a head gasket, but the pressure test came out fine. So he said the next most reasonable thing was a thermostat, and I said "go ahead and do it". (I should have told them to put in a 195 instead of stock... too late now). It turns out it was the thermostat. I wish I had had the time & tools to just give it a go, both for the experience of working on my car, and for the approximately $100 I might have saved.

A little speculation: The reason I didn't believe it was the thermostat is that it didn't fit either the symptoms for stuck open (won't warm up, or at least slow to warm up) or stuck closed (the radiator hoses should not get hot, and the car should not cool down under low-load conditions, I think). So my new theory is that the thermostat was opening and closing at the proper temp, but it was not opening as far as it should (maybe only opening a very small amount). What do you think?

Certainly sounds plausible. What is the temp rating of the stock thermostat? I also wonder if this is why American cars seem to have better working heaters than Japanese. Every American vehicle I've taken apart had a 195 in it, even my old 74 Chevy. I've never owned a Japanese vehicle.

-Jay

The wax in the thermostat could have leaked out a bit causing it to not open all the way. On smaller 4 cylinder cars though, you can still cool the engine down by running high-rpm low-load conditions. Enough water gets blown by the thermostat to cool the engine down somewhat even with the thermostat fully closed in most cases.

Headgasket? Seriously? I had a mechanic tell me that once because he'd tried 'everything' and couldn't figure out why there was so much pressure in the cooling system. I told him the cap wasn't purging and he insisted it was the headgasket and that it'd be $2500. Turns out, he put the wrong radiator cap on it and it was in-fact not purging resulting in 40+ psi in the cooling system.

After that, the engine started boiling over and he was SURE that it was the headgasket and that this was further proof of that. The thermostat needed turned 90 degrees and it has worked for the last 40k miles like that.

I don't trust mechanics.

stuck thermostat is my guess.

I agree with much of that sentiment, but this guy looked at the vehicle, and has some reason to believe it was the head gasket (as did I), but then, instead of saying "It'll be $xyz for a head gasket", he tested his theory, and charged me $50 for the test (I feel that was a little high, but lots of other shops would have charged me $100 for "diagnostics" when all they did was check for CEL/MIL codes & a quick visual inspection).

EDIT:
Jay--It is a 180 stock, IIRC. Other temps available were 160 and 195.