Strange electrical behaviour on a 214

(sorry for some terms, I'm italian and I don't know the exact translation of tech words)
Something odd is happening to my 214 SI (1991 model).
Yesterday the "battery" light on the dashboard (I mean the light with the battery on it, I think it refers to the alternator or the battery recharging) went on. I kept on driving ten minutes, then the engine hiccupped, slowed down and stopped. The lights were dim and the engine didn't start again (the starter electrical engine didn't run), so I thought the battery was gone empty (because the alternator wasn't working, hence the light on the dashboard).
Some hours later I checked it out again, and... surprise! :-o The starter electrical engine ran, the engine started, and everything looked fine. So the battery wasn't really empty, after all.
Today the car started fine again, I drove it for some minutes and then - again - the engine hiccupped and stopped.
I suspect there may be something going wrong when the engine warms up: when it's cold it's ok (although the battery light on, has to mean something), when it becomes hot something happens (maybe a short circuit...).
I inspected the engine, I didn't notice anything strange (but I didn't know what to look for, actually).
Did it happen to anybody else? Do somebody has some hints?
I'm on a very tight budget, so I would like to do the repair by myself (if possible).
Thanks in advance, Valter from Italy
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