I have not rebuilt my heater box so I cannot confirm this works for that purpose, but I have used Dynaliner for other purposes in my truck. It's closed cell so it does not soak up water and it is heat resistant (made for use under the hood). I've personally cut out a square, put it on a food scale, soaked it in water, and weighed it again. It does NOT absorb water and after 1 year under the hood it looks as good as the day I put it in. The adhesive seems to work well but if you wanted to be extra sure it stays in place grab a can of 3M spray adhesive from Amazon or any big box home improvement store.
Dynaliner 1/8" thick from Amazon link