Cobra 1

Have you properly burped the air out of the system by removing the vent plug on the coolant crossover tube? You may need to do this multiple times to completely burp all of the air out of the system...

How's your belt? Could it be slipping?

Being in Canada, I wouldn't expect this to be a problem, but '96 Cobras did have a heating problem that was serviced through a TSB. People with '96 Cobras living in or driving through the southern United States, particularly the Southwestern deserts experienced a heating problem that was resolved through changing a bunch of parts under the TSB. The OBDII is programmed to dial back timing, then shut cylinders down to "save" the motor when the car is overheating (According to what SVT told me at the time). Not sure if this could explain the alternator/charging condition you described.

Start with the service work done at the dealer--was it done properly, then consider how hot it might be. I only had a heating problem in the Mojave desert, but had the TSB done to my car because I may have to go back through the Mojave at some time...