How to heat the air inside of a plastic tub

[hamsterman]

From what I have read, it is a bad idea for a heat lamp to be resting on a plastic surface. Perhaps I could just make a circle of heat resistant tape on top of the bin so that the heat lamp rests on top of a thick layer of tape rather than coming into direct contact with the plastic lid?

Here is my improved idea.

Problem 1: The metal heat lamp may melt the lid if it rests on top of it.
Solution: Have the heat lamp rest on a circular layer of insulating, heat resistant tape.

Problem 2: The heat radiating from the lamp may melt plastic that is directly in front of it, or plastic directly in front of the heat lamp may prevent optimal transfer of heat into the bin.
Solution: Replace the plastic under the lamp with mesh, or poke many holes into the plastic below the lamp.

Can anyone think of additional problems that I have not thought of, or if my solutions are insufficient?

You could use a radiant heat panel. For quarantines I have placed tubs in a larger tub or enclosure with a radiant heat panel on the top of the larger enclosure controled by a tstat.

Your dual-enclosure idea sounds good, but I think there must be a way to miniaturize that setup. Having an enclosure within an enclosure seems like a waste of space.