If you like the GT6, please don't let fear of it being too hot in the cockpit deter you from buying one. If the firewall and tunnel cover are sealed and insulated properly and secured with the correct hardware, the GT6 driver compartment is no hotter than any other (non-convertable) LBC.
A/C was a dealer-installed option on a limited number of GT6s and A/C can be fitted to a GT6, but it's not often encountered. I'd assume that a modern A/C unit could be fitted, but I've never seen one.
Also, a significant number of GT6s were fitted with a factory folding roof. Many of these cars were shipped to Austrailia and S. Africa, but they're rare in the U.S. However, a folding roof with the same dimensions and better quality than the Triumph factory model may be fitted to a GT6 for a fairly resonable cost and it's a great option to have. I plan to install one in my car.
I don't want to sound too obvious, but if you want a convertable, don't buy a GT6. But, if you want an affordable, exciting LBC, the GT6 is an excellent choice. Fast, fun to drive, readily available parts, and lots of resources for repair and maintenance.
Good luck, let us know how it goes, and welcome to this great forum!