Last June, I found a 72 GT6 on Ebay that happened to be near my home town, Oklahoma City. I bought it for $2,400. It ran, more or less, and was roadable. It had a pretty good paint job and interior. I was able to drive it home, unlike most of the British cars I have bought. After a tuneup, some steering, wheel bearing work and other miscellaneous fixes, it became my preferred daily transportation. I am 6' 1" and have no problem sitting in the car though getting in and out is not easy. As to summer heat, none of my British cars (except the XJS) have air conditioning, so I guess I am accustomed to the heat of an Oklahoma summer. It is just as hot in my Healey - seems hotter, in fact, with the top down.
$6,000 seems a bit high to me. For that money, you should get a car that needs absolutely no mechanical repair and has decent paint and interior. Everything should work.
One thing I found is that the GT6 really needs an overdrive transmission. On a non-overdrive car, the engine turns 3,500 at 60 mph. Interstate speeds around here are 75 mph and up. I don't want to push a 35 year old engine that hard so I limit my highway speed to 60-65 mph. Last month, I bought an overdrive transmission, to be installed this winter.
One big advantage of owning a Triumph of this era is the availability of parts at reasonable prices. In my experience, parts are generally half or less the cost of similar items for other makes of British cars.
If you decide to buy this car, I have no doubt that you will enjoy it very much. However, if it were my bucks, I would still be looking. Best of luck.