1983 944 heater stays on, where to start ?

Fan switch,or the reostat is stuck at the blower motor, pull blower fuse to stop temperary untill you find the issue.

i should have been more stated that heat come out still when fan is off, some kind of flapper stuck open ? and the dash has to be removed to access ? If so where to start ?

Fan switch on the back of the radiator, up top on the drivers side, has gone bad. Tough to get at, but a common failure.

I should also mention the vacuum actuated heater control valve at the back of the block on top, is also a common failure point due to old age. Another tough to get at item. Parts should be easily available. To the fan switch problem: the switch itself can be either a two lead harness connector or a 3 lead connector. Pull the connector off to find which switch to order. Most of the older 944's had a two lead connector. Hope you have skinny arms for this job. Good luck.