We dealt with that situation the first years we were processing and used our garage as a cutting room. To thaw the frozen deer we would put tarps on the floor in our hallway coming in from the backdoor and leave them overnight.
    If you have a heated basement you could do it down there. I definitely would not use a heater, not only because of the smell but it would not provide an even temperature surrounding the carcass.
 The way we thaw them now (the best way I've found) is to hang them in our cooler. It takes about a week but there is minimal moisture loss. 
    Good luck.

Dave