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Radiant heat on top of existing slab
My house is a single family tri level built in the late 1980's in northern Illinois. My lower level (even with the ground) is slab on ground and is where we spend most of our time. The family room with wood fireplace, laundry room, office, 3rd full bath, front and rear doors. My house is a fairly open floor plan with the 13'x 24' family room flowing into the kitchen on the mid level (3 steps up). In the winter (25* and less) the carpeted floor is cool to the touch and the lower level is a good 5*-10* colder than the mid level of the house. I have 2 forced air gas furnaces now (one for the top level, and one does the lower/ mid levels). I want to eliminate the carpet on my lower level and go with tile which will make this cold floor issue even worse. I am not looking to raise the temp of the room as much as make the floor warmer. I am a plumber and will be doing all the work myself even though I have not done much heating work. I have started looking into installing radiant heat under the tile but would rather not tear up the existing slab. Loosing Height is wanted to be kept at a minimum (as always lol). I was liking the Roth panels, but I cannot find it for less than $6/ ft, and with having almost 700 square ft thats a bit too expensive for me. I have another issue as well which made me look at a composite solution, while I am not in a flood plain the river is about 1/4 mile from me and 3 times since the house was built the river has come up to say hi. The last time was 2013 (a month after I bought the house) and if I had not sand bagged the house I would of had about ankle deep water on this level. I plan on installing a more permanent flood defense solution than sand bags, but need to keep in mind that things happen and only want to do the floor once if I can. What is my best / cost effective solution?