1988 Lincoln Continental Dies when hot outside.

First off let me name the parts that have been replaced in the past year, just tested codes on the engine, only thing that came up was a bad oxygen sensor which was replaced yesterday. This is a 1988 Lincoln Continental 3.8L 6 cyl. Mileage: 125,300

New:
Battery
Alternator
Voltage Regulator
Transmission
Water Pump
Radiator
Oxygen Sensor
Oil Change
Spark Plugs, Wires, Cap
Engine is original from 1988, but has had a lot of work done to it in 1998 (Heads replaced ect)


Anyways the car will run fine at night time, I took it for about a 2 hour drive to another state yesterday and it ran fine the whole way. Never died at a stop light or acted like it was going to. I get off of work today around 5pm when the sun is beaming down hard and it's about 80F outside, I started the car and it shuts off after running about 10 minutes. I let it cool down a bit and drove it about 5 miles away without stopping and it seemed like it was running fine. As soon as I come to a stop or if I'm going around 4-5MPH it will die on me. When I try to start it up again it will start but then die again in about 10-15 seconds. The fuel pump comes on when I turn the key over so I don't think that's the problem. This has been going on all winter but Is getting worse since it's getting hotter outside. My radiator and reserve tank is full, and not leaking anything at all. I was just wondering if anyone could know what the problem is.