I have a 1998 Oldsmobile Regency. The alternator was causing the positive cable on the battery to be extremely hot. I replaced the alternator,but the battery light on the dash is still on.

How do you know it's surging? In any case, about the only thing that can cause this is a faulty regulator in the alternator, or a poor wiring connection (e.g. battery cable or at alternator).

Turn off and check positive cable for wear, if the cables outer covering is damaged, it can short to the chassis or other metal parts of the car.. and cause the cable to heat up. Leave it in that sate long enough and it will eventually melt. or in extreme cases cause a fire. If you find any damage, then replace said cable immediately

reset the CPU is done with a code reader as the program may be corrupted and tapping the negative will only make it worse.

you change it from under the car

You need to test your charging system circuits at the alternator. (see diagram and instructions)

BLK is the cable to the battery POSITIVE terminal - this is hot at all times.
PINK/BLACK comes from Fuse #5 (15 Amp) in the relay center under the right side of the instrument panel. This wire is hot (battery voltage) with the ignition switch in the RUN, BULB TEST, or START positions.
BROWN comes from your instrument panel and is protected by Fuse #16 (20 Amp) in the instrument panel left side fuse block. This wire will have slightly less than battery voltage with the ignition switch in the RUN, BULB TEST, or START positions.
If any of this is not as described, let me know what you have found and we can continue if needed.

if the battery cable end have corosion on them the current is not able to charge battery. If you put a multimeter on volts dc 20volts and the car is running and charging properly, the meter should read approx. 14.73 volts. Clean the inside of the cable ends, and the posts on the battery with a wire brush, then coat all of them with some vaseline. Hook them up and tighten. If that doesn't work you will probably need the diagram, to trace a dead short.

the filter is in the filter box next to the battery eather unscrew the screws if it has them or pop the clips it will open replace the filter

Sounds like the heater control unit is going bad. I believe this unit has a digital/vacuum control unit which explains why you are only getting hot out of one vent. Try the salvage yard or ebay for a replacement unit. They are non-repairable...

EITHER U HAVE A OPEN ELECTRICAL CONNECTION THAT IS HEATING UP AND GROUNDING TO SOMETHING REDUCING THE VOLTAGE. CHECK PARTS THAT R CONNECTED DIRECTLY TO THE BATTERY AND THE PATH OF THEIR LINES.STARTER , ALTERNATOR.

I dont know if this will help but vI had the same problem with my farm tractor It turned out to be a short in one of the wires cant remember vwith one. try tracing them from the batery back