Your issues though is the cold side not being in the 80s?

If I understood correctly then you would probably have to use more heat tape on the other side too like you suggested but set on a thermostat for 81-82F. Is the room they are in occupied? Do they take a separate area of the house if so a cheaper solution if you do not have a two slotted thermostat would probably be to buy a little room heater from a store and use it to heat the room.

You could replace the tape that came with it but with all I have heard about heat tape and my limited experience(Just got my first rack) I worry about the potential safety/fire hazard non-recessed tap could have if your resting the bins on them it would leave patches of tape not able to properly have heat escape.