'87 4kq: whine, then stall

[Andrew Buc]

A few days ago I was driving home from work on a hot (mid to high 80s) 
day. After about 5 miles I suddenly heard a loud whine from the rear of 
the car for a few seconds, and then the car died. I was able to restart 
with no problem, and as I was a couple of blocks from a store where I 
had to stop anyway, I found a parking space. Half an hour later I was 
on my way again, but I got the same symptoms 5 or 6 times in the 
remaining 5 miles home. I found that each time I restarted, the car 
would run for at least a little while. This also happened under more or 
less the same circumstances a few weeks ago, but the car stalled only 
twice, and I don't remember if the whine was present.

Suggestions as to what I should check first? Thanks.