No insulation under the slab, was built as a summer camp cabin, walls are now insulated and structure is pretty tight. Would be used as an office. Losing three inchs of floor would creat a big problem with front doors as there is no head room to raise them
What are your fuel options, and what is your design-day heating temperature? (Or what are the temps at the coldest hours of the heating season that you anticipate needing to maintain temperature?)
With no insulation under the slab radiant floor is pretty wasteful- you can do it, but it won't be very efficient. (If electric, it'll be ATROCIOUSLY inefficient- you lose 60-70% at the power generating facility, then half of the energy that actually reaches through your meter ends up heating the ground below your building!)
That said- if its very dry & sandy soil you may be able to do OK with radiant if you insulate with 2" XPS down to couple of feet below the usual frost line depth around the perimeter of the slab, making sure that the slab-edge is fully covered. (How easy/hard it is to get right depends on a whole lot o' particulars.)
But unless you're working the wee hours a lot, it's probably better/cheaper to go with something with a quicker response than radiant-on-slab and use nighttime setback for improving efficiency. The thermal mass of the uninsulated slab and some depth of subsoil will have to be maintained at temp pretty much 24/7 to stay comfortable thoughout the 9-5 workday. Even a propane-fired 65% AFUE side-vented wall furnace would probably be cheaper to run than radiant in this application (and a whole lot cheaper to install!) Using an insulating floor covering like cork or carpet can sufficiently take the edge off the coolth under foot, unless you're prone to working in your socks (which might become habitual, if you have radiant floor!
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