98 sunfire needs jump to start

98 sunfire convertible 2.4 engine
car will sometimes not start, will not turn over. Will start when jumped. Checked battery at 12.7 volts, low 13s at idle and around 14 when revved up. I ran it few just a couple of minutes and alternator was very hot. Also, brakes tried to lock up once.
I thought this sounded like a bad alternator. Thought maybe brake problem caused by low voltage?? Any other thoughts or ideas as to the problem? Thanks

also automatic tranny

I would check both battery cables and your ground. Also check the wire to the alternator. It may be corroded and causing feedback when charging. High resistance will cause the alternator to get hot. Clean everything and put is back together. Also if your battery is more than 4 years old you may want to replace it as soon as possible because it may be slowly dying.

thanks, havent had a chance to look at it, have another battery, will try replacing that first and see waht happens.

The voltage should not vary a whole lot comming out of the alternator. It should always hover around 14.5 when running depending on whats drawing power. ie. AC, lights, fan etc. If you measured 13 volts across the battery that's too low. Look for a loose wire to the alternator or a corroded wire. Have the alternator tested at AZ, Advance, etc etc.