I have central air, and the outside unit (condenser right? I'm a complete noob) kicks on for about 30 seconds, then stops for 30 seconds, then repeats.

This doesn't seem normal. Advice?

Thx!

Is it a heat pump?

I would cut the breaker to it until you have time to find and fix the problem. My guess is that even with the crankcase heater, you have liquid in the compressor and it kicks on, over heats and kicks off, cools, and starts again. Very bad.

First thing is to check for 24 volts between the Y and B or C terminal at the furnace. If so, then disconnect the yellow wire from the thermostat and see if you still have the 24 volts. If not, and it is set to heating mode, the thermostat or wiring has a problem. If so, the problem is on the control board.

Yes, I have tripped the breaker in the meantime.

Thanks for the tips, I will check them out!