Good that you plugged them back in, they're the only extra measure of over-heat protection the vehicle has, and are also need for correct A/C operation.

Make sure the plastic tube going from the top of the radiator isn't plugged up with silicone sealant. This tube ends up at the expansion tank next to the firewall, coolant MUST freely flow through it to get the air to the tank and out of the system. Remove the expansion tank cap and try to see if coolant is flowing into the tank with the engine running from that port fitting.
I've seen silicone get stuck in the tiny upper radiator fitting from people using it to seal a new water pump or some other coolant part. Risky stuff to use on these vintage BMWs, too many small coolant passages to get lodged into.

If it is a bad thermostat, just remove and test it as others have posted.