Would a high temperature heat resistant tape be able to insulate a heating wire (heated at maximum 80°C)
Kapton tape is good up to 400C. However it's not great when subject to wear (wikipedia):


  Kapton insulation ages poorly: an FAA study shows degradation in under 100 hours in a hot, humid environment.[6] It was found to have very poor resistance to mechanical wear, mainly abrasion within cable harnesses due to aircraft movement. Many aircraft models have had to undergo extensive rewiring modifications--sometimes completely replacing all the Kapton-insulated wiring--because of short circuits caused by the faulty insulation. Kapton-wire degradation and chafing due to vibration and heat has been implicated in multiple crashes of both fixed wing and rotary wing aircraft, with loss of life


And of course connecting a homemade electric blanket to the mains whose insulation may wear out is a good way to accidentally kill yourself in your sleep.