cooling question

I just got a new radiator and thermostat put on. It is around 0 degrees outside and it gets up around 220 in the city, which Ive read is normal, but even when its that cold out? And when I'm at a light the heat gets cool and then when I go its gets hot again. Is it just because its cold outside or what? Also, the AC light comes on when I move the directional control to the very right. Move it left and it goes off or I can shut it off. Leave it and the light stays on even though I'm hitting the button. Any ideas?