Yes, indeed resoldering the CC unit MIGHT fix the problem. But you need to check the current draw of the auxilliary coolant pump that is located on the passenger side fender well. It should draw no more than 1.3 Amps. If it is drawing more than 1.3Amps, it probably knocked out an active component in the CC Unit. In this case, you should replace the pump and CC unit. If the cooling system is dirty, you might get lucky and be able to remove and clean and flush the pump and get the current draw below 1.3Amps saving that portion of the expense.

Good luck,