OK, according to Kodak T-Max stock stored in a half full bottle is good for 2 months. And this is based on normal room temperature.(posted 8848 days ago)And I made a mistake, according to Kodak mixed stock Fixer is good for only 2 months, and the working solution for 1 month.
SO figure that Kodak is somewhat conservative with its ratings. Also for chemical reactions figure that for every 20 degree drop in temperature, things go by 1/2, so the keeping time should be doubled. So if you put the chemicals in the refrigerator you get more than twice the life.
The quick and easy way would be to shoot a 24 exposure roll, and develop it. If it works, use it. If not, toss it and buy some more.
BTW many people prefer Xtol to T--max developer.