The car's heater doesn't work and when the a/c is off the engine temp gauge goes up. The car had just came out of the shop with a new radiator any suggestions on how to fix this myself?

 

Well if there is air in the system you're going to end up having higher temps. Perhaps they didn't bleed/burp the system after the new radiator, or bled it but didn't let it bleed through a thermostat cycle. Air in the heater system will cause no heat since there's nothing flowing heat through the heater core. I'd assume when your A/C is on your fan goes into high speed like most vehicles, so when A/C goes off and fan operates normal you're not cooling off as much.

I'd take it back and say "Fix it" since that's not right.

 

yep, bleed, bleed and re bleed. sometimes that air can be a pain to get out. specially if the steam tube is getting plugged. did the shop flush the cooling system before installing the new radiator? if so did they flush the heater core separatly or the system only.