I put in a new battery but while driving heater and radio shut off

Clearly any additional electrical demand on the system is enough to disrupt the power needed to fire your spark plugs.I would check the alternator output first.There are so many things that it could possibly be that I think you should take it in as soon as possible and have it looked at.This could get very dangerous if it should happen at highway speed during rush hour. Good Luck

Sure!
I have the same problem.
Problem is, that radio is not wired into your car's electrical system properly to cause this.
Rather than take it to an expert for $$$$, I decided to do this.
I pulled the radio head out and found the hot wire ( it was red) and put an inline shut-off switch there that is mounted below the radio on the dashboard.
That way, I can shut off the drain whenever the car is parked.
Be Blessed.

Check battery wires for tightness. That sounds likely to be the problem

Have you had your alternator checked ?
If there is no charging from the alternator the "problem" will be solved as long as the new battery retaing its voltage. As soon as you start to use power you drain the battery. it's a bit like putting air into a punchured tyre ..... its still punchured . Could be your original problem ! ! Good luck

Check your battery and cable and ground connections. check also your alternator belt (drive belt). Have your battery checked at any autoshops.

Sounds like the battery is bad. It's pretty common to lose a battery and alternator at the same time.

Alternator is getting weak... i would reccomend a rebuild on it, thats the cheapest, or put a new one on it before it leaves you sittin... when your alternater gets weak thats what it does, its not putting the correct amperage back to the battery, and the battery is making up for what the alternater isnt putting out... hope i didnt confuse you, and hope this helps

It does seemed a problem with the wiring. Check for any loose connection or bad insulation.

I have had the exact problem. I've changed altenator 3 times also and it has the same leak, but I've changed altenator an batterys over 2 year span. It just happend to me today after not driving it for 5 months. It's been in storage while I was away. Drive it fine for 2 days but today the radio kept shutting off and finally the car died right in the middle of the road. Bought a new battery because I had a warranty on last battery, but bought it just to get it home and in the driveway. Did you ever find out what was wrong with it?

put a new battery terminal on it and check your alternator