Plastic protects from wind and frost but deep cold will make the plastic work against you. If the plastic touches the plant it freezes that part that it touches. Since I don't like to depend on the electric company in storms, I go unheated under cloth Better insulation value with unheated cloth over unheated plastic.
During the big freezes in the 1980's, some trees under plastic without heat had the worst damage. Unless you take the plastic down the plant will get more heat and be more active when cold hits.
The time it takes to kill the tree depends on the type of cold, how low it gets for how long and most forgotten, is the tree more dormant or full of growth. Cold for a week before freezing is better than 80's until a big freeze.
Cloth will last longer than plastic in that it can hold any ground heat and keep it longer then plastic. I use quilts and put them on and off depending on need. Keeping them off the tree itself as if cloth gets wet, it can damage anything touching it.
The heat source under plastic works, if the electric stays on.