Heat mat for bin / diet for discoids

I live in Florida and I'm trying to breed discoids. Currently I have about 30-40 medium - full grown adults in a 10 gallon with a bunch of egg cartons. I have them in a tank and not a bin because from what it says on the package the heat mat should not be used on plastic. While they seem to be doing ok in there right now, I just ordered 100 roach maternity ward, and 2 shipments of 50 small to medium and I fear that the 10 gallon wont be big enough. Can anyone link me to a heat mat that I can safely leave on the bottom of a decent sized moving bin that will keep it at 90-95 degrees. I will be at school for most of the day and wont really be able to keep an eye on the bin so if it were to start to melt of even worse catch fire it could be very bad. Is a heat mat like that even a thing or will I just have to hope I can find a bigger tank? It might be a bit though because discoids are super expensive and I also bought a big jug of water gel stuff so my budget for bugs is too low to buy a 20 gallon or up. If anyone knows a good heat mat I would love it if you could link it or provide enough details that I can easily find it, I have very bad luck when it comes to finding stuff online. Thanks

Edit: What is a good diet for discoid colony? currently I have that diet for crickets that comes in a big 6 lb jug from flukers. They seem to eat it but is it healthy for them? What fruits and veggies should they be eating, keeping in mind that they will be feeding my beardie. Currently I give them a peeled apple once a week and sometimes an orange if I have one. Last thing is the bug burger stuff really that good? I see a lot about it while looking at discoid roach colony videos.

Also I just found a heater from my last house up north, It has a setting to heat until 85 whcih gets the inside of the tank to about 90-95 up closed to the side facing the heater, will this be good enough? its like 85 at the cool end, 88 at the start of the egg cartons, and around high 80s to mid 90s up close to the wall facing the heater. Theres one more setting max but that makes it very hot inside for closet and like 95-100+ in the box twords the heater but would be expensive to run / idk what temperature max is or if it even turns off once the room reaches that temp.

I don't know about the heat mat, but as for the food, I would think any food you would feed your beardie would be good for gutload. They also need a source of protein - so oats or bran, maybe some cat food or fish flakes. You can find roach chow online that will be good, particularly if the seller also breeds discoids.

The cricket diet is probably fine.

I think the Repashy stuff would be fine, but I haven't tried it.

I think the heat mats you can use on bins probably cost more than a 20 gal tank. The heater you found sounds workable (*not on max). Mine love the bug burger, but dry, not made into gel. I just put the powder in a little dish for them. That gives them enough protein, and I give them the same greens and veggies as my dragon gets. They get his leftover ones at the end of the day, plus fresh ones so there's enough for everybuggy. :0)

I've seen people use heat tape, would that be an option?