cavity wall insulation in an "internal" wall

fil212

The downstairs of our house has a integral garage with a cavity wall dividing it from the rooms. The cavity wall goes to the roof line. We think some heat is leaking into the garage and every time it snows there's a line of melted snow on the roof in line with it. Should I have it insulated?
Come to think of it, there are two bedrooms above the garage, am I losing heat through the floor too?
Thanks

maninthestreet

Are you sure it's a cavity wall? I have the same sort of arrangement, and the wall does not have a cavity. I partially solved the 'heat loss' problem by sticking depron foam to the wall on the garage side.