1987 thunderbird won't fire

i have a similar problem, my 87 t-bird will run sometimes all day and then sometimes for only 30 mins or less before it dies, and when it dies it wont start back up unless i let it sit for a good while, it blows my mind because when i got the car it ran great, it was ugly, but it ran like a champ, well now i got the body fixed and was on my way to get it legal and it died on me, it sat on the side of the highway for a week, and i got a ride back to town and stopped to see if it would start and it started right up, i drove it home and right when i pulled in the driveway it did it again, died, and wouldnt start back up, well for a while i delt with this, driving it short distenses visiting friends and whatnot, but then it just got worse and worse to the point that if i drive it to a friends it usually dies half way there and i have to walk the rest of the way, really sucks when its freezing cold, pitch black out side on an old country road in the middle of nowhere with another mile to go down the road, well that was the last time, so on the way home, (few hours later) i started the car right back up and drove it home, didnt die the whole way, wow, anyways i wasnt going to get stranded like that again, so i just parked it in the front yard, its been sitting there for about 2 months now, i was starting it up everyday so it wouldnt rot, but most of the time it dies after a minute or 2, so all that killed my battery and i havent started it since, it sort of acts like its over heated, because once it dies it wont start until a few hours later, but all my fluids are good, probably needs an oil changebut thats it, and the meter inside says its running in a normal temperature range, idk... any thoughts? i heard it might be the fuel pump, but that doesnt make sense to me.. any reason that it could be? if its the fuel pump then that could very well solve both of our problems

-steve i have a similar problem, my 87 t-bird will run sometimes all day and then sometimes for only 30 mins or less before it dies, and when it dies it wont start back up unless i let it sit for a good while, it blows my mind because when i got the car it ran great, it was ugly, but it ran like a champ, well now i got the body fixed and was on my way to get it legal and it died on me, it sat on the side of the highway for a week, and i got a ride back to town and stopped to see if it would start and it started right up, i drove it home and right when i pulled in the driveway it did it again, died, and wouldnt start back up, well for a while i delt with this, driving it short distenses visiting friends and whatnot, but then it just got worse and worse to the point that if i drive it to a friends it usually dies half way there and i have to walk the rest of the way, really sucks when its freezing cold, pitch black out side on an old country road in the middle of nowhere with another mile to go down the road, well that was the last time, so on the way home, (few hours later) i started the car right back up and drove it home, didnt die the whole way, wow, anyways i wasnt going to get stranded like that again, so i just parked it in the front yard, its been sitting there for about 2 months now, i was starting it up everyday so it wouldnt rot, but most of the time it dies after a minute or 2, so all that killed my battery and i havent started it since, it sort of acts like its over heated, because once it dies it wont start until a few hours later, but all my fluids are good, probably needs an oil changebut thats it, and the meter inside says its running in a normal temperature range, idk... any thoughts? i heard it might be the fuel pump, but that doesnt make sense to me.. any reason that it could be? if its the fuel pump then that could very well solve both of our problems

-steve