A weird (battery/alternator) problem with Toyota Starlet 1985 :(?

Sprinter

New member
Its a 1985 Toyota Starlet 1.0L 12V version with 180,000kms on it. I had been driving this car for over three months now, never have had any problem so far.
But today I drove to a friend's place and car refused to start, I jump started it with my friend's car. And when I reached home I noticed the car was over heating (the temp needle was just a mm short of H), I switched it off, checked the battery terminals, coolant, engine oil etc, everything was fine. The car started again (without jumping) I drove a few kms the engine did not heatup but suddenly it felt like battery ran out of charge as the headlights dimmed, the heater stopped, the turn signal lights refused to work. I somehow managed to drive back home, without turning the engine off I switched the headlamps, heater, stereo etc off and it suddenly felt that alternator started charging again, lights, heater etc started working fine. I switched off the engine started back again, and everything was working as it should.
I am really confused, no idea what's wrong does it sound like battery problem, failing alternator, wiring problem or something else?
One things I would like to add. The timing belt is due and I have to change it this month.
The alternator belts sqeeks in cold mornings.
 
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