Interesting Problem

I have an interesting issue with my '93 Ford Thunderbird. It's a 5.0 liter, V8, with 203,000 miles on it, which very well may be the issue. It's just a little old.

But anyways, on to the issue.
Everything ran fine with the car, no issues, until one day the heater core went out, and it pumped exhaust and coolant into the cab. Easy to clean, I replaced it, and switched from a 180 degree thermometer, to a 160, which the owners manual said would work just as well. The car ran fine for a couple of months, and then stalled on me one morning. The stall happened as I went to accelerate from a stop. Prior to that, that morning, the car hesitated really badly on acceleration, and sounded like it wanted to die. I took it into a dealership, had them look at it, and they told me, eventually, that I needed to replace my mass air flow sensor. Not knowing any better, I did so.
600 dollars later, and after no less than FOUR trips to the same dealership, the car still has the same problem, and they couldn't pinpoint it. Furthermore, on a suggestion from a friend, I took the car to a transmission shop, to have it serviced, and the gentleman there plugged a diagnostic scanner up to it. One of the problems that came up, surprise, surprise, was the mass air flow sensor.
Now, the car can run just fine, but only if I let it sit in the driveway and warm up first, which can take up to half an hour. Also, the heater doesn't heat up independantly anymore, like it used to. Now it won't heat up unless the engine is warm.

So, gentlemen, there it is. Sorry for being so long-winded, but I didn't want to leave anything out. Any comments or ideas are appreciated.
Thanks!

The thermostat should be a 195 f. The computer need to see that to go into closed loop.

i'd say your throttle position sensor on the throttle body is the likely culprit. change it and have it calibrated.