Converting shoe shelf into a rack, need some advice

Hello, I've found a neat 4 tub shoe rack from the container store and am interested in turning it into a rack. Unfortunately for me, I only found it AFTER i had ordered some ultratherm heat pads. Otherwise i would have had custom heat tape made.. lol.

Anyways, I think this system could work but I need some tips from the pros. I currently do not have any BP's, this is why i am preparing now, so there'sno rush.
How would I go about using the heat pads with this shelving system? I read somewhere on here (I've read so much info that its all melting together) That people tape on a type of backboard made of corrugated plastic to the heat pad. Do I need to do this?

I will post pictures as well to show what I am working with, and if anyone else fancies to do one of these as well.
The tubs I have have little feet on the corners to raise them up a little. This shelving is made of melamine, my concern is heat build up from the heat pads is there a general spacing rule for these?

Another concern I have is how exactly do I mount the thermostat probe to the heat mat? And what should I do to stabilize it so the tub isn't lop-sided with the tstat probe under it?
I have no problem modifiying the shelves witj a router or dremel to make things work, but i am not sure on how to go about it. Any tips or ideas would be wonderful.
Thanks!

P.s. hope the pictures work, im new to using tapatalk apphttps://uploads.tapatalk-cdn.com/201...8bd23122c3.jpghttps://uploads.tapatalk-cdn.com/201...56a53313ce.jpghttps://uploads.tapatalk-cdn.com/201...e91dfd4902.jpghttps://uploads.tapatalk-cdn.com/201...ac2eafa706.jpg

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How flimsy - or not - is the plastic the rack is made of? That top shelf looks like it has enough of a gap to allow an escape.

The tub is stiffer than a regular sterilite, but not by a lot. I had same concern which is why i showed that angle. What is the usual height allowance?
I could fix that gap easy enough, i left it as is because i do need space for the uth and probe for the middle shelf.

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