Burner lights buts goes off after a few minutes

Cleaned external vent pipe vacuumed out lint tray think thermostat is bad

I think your diagnoses is correct on the thermostat being bad. But check a few more things.

If you remove the vent hose from the back of the dryer and let it run, does the burner shut down as you describe?

Are you certain there is not a clog in the "duct" within the dryer itself? The lint filter appears to be located at the bottom front of the dryer, just inside the door. There is a bell shaped plenum that the lint filter fit's into, that turns and points towards the bottom back of the dryer. Is that duct system clean?

It could be the temp switch, cycling thermostat, or the over temp limit. Considering how the unit is operating, the only way to tell which one is failing is to measure the voltage across each one while the dryer is operating. When it opens (meter reads voltage), watch to see if it ever closes (meter does not read voltage). The cycling thermostat should open and close throughout the drying process, but it could hang open. The temp limit should not open unless there is a duct clog, but, then it should close after cooling, acting like a cycling thermostat. It could also hang open.
Of course, the temp switch is only a switch but it could be bad intermitantly.

Each of these components is not too expensive, so you might just want to buy all three.

Let me know what you find.