What kinds of plants are you growing?

I think that generally, one is encouraged to remove the heat mats for two reasons:

1) higher heat encourages faster growth, but if light is insufficient to support this growth, the plants will tend to be spindly, and

2) as the plant growth increases, water demand increases, and bottom-heat plus increased water demand will make the plants dry out faster.

I usually find that my fluorescent tub lights put out enough incidental warmth to keep my seedlings in the basement warm enough.

But I have also in the past draped my lights with reflective mylar with a small fan for air circulation. This would have the additional advantages of higher light levels due to the reflectivity of the mylar and encourage sturdier plant growth by the slight agitation from the air movement.

I might experiment with your latter idea if it is not too much trouble.

I have a cat heat mat that has carpet on the top. I have been using it under some of my Red Robin tomatoes. It was under all of them until I re-potted them in to one gallon pots.

There wasn't enough room for all of them in bigger pots. They are about 18" tall now.

It is supposed to be at a cat's normal temperature, so that would be around 100 degrees. I think the carpet acts as a buffer, maybe kinda like your idea of a mesh tray? And all of the plants are sitting in old cookie sheets for bottom watering.

The toms on the mat have much thicker stems and are much greener than the ones on the cold counter top. The temps in that room are around 50 degrees average.

I swapped them around over the weekend to see if the others will thicken up their stems. I left one on the mat, it was starting to bloom.

I hope my 2 cents helps!