Are you judging the temperature of the dryer by feel or a thermometer? I understand your concern but it may not be as hot as you think. The smell comes from the lint that may have collected in the dryer cabinet and was disturbed by your work before. It would be a good idea to open the cabinet again and use a vacum cleaner with a brush attachment to clean out all lint.Then, with close observation, run a load of towels expecting to smell a little schorching but a second load should not smell.
Rustedbird has a valid point about the fire danger; that's why I said "under close observation". The UL label means a house fire would not happen but be contained in the dryer cabinet. Still, it doesn't hurt to take precautions; you have a 10 lb fire extenguisher, don't you?