Can't help thinking that perhaps there is something wrong with the belt, especially as you say that it seemed ok on initial testing. Which suggests that to me that a fault has developed.
Excessive heat suggests something binding somewhere as does having to release the tension to allow the motor to start.
I assume that the sander motor is an induction motor whilst the drill motor, assuming a hand held pistol drill, will be a series wound universal type of motor and hence totally different, a bit like comparing cheese & chalk.
I have a vertical drilling machine with a 180W motor which can be fairly easily be stalled. However, when stalled, the motor complains with rather loud buzzing sound. As indeed do my pistol drill and portable electric saw. What does your motor do when stalled?
Sorry, can't be much more help
Peter G. Shaw