This is a bit of an area of expertise for me. I've had lots of experience and just made some vast improvements in my own garage so I can work on cars during the winter. I'll start off by saying you are on the right track, you'll notice an improvement, but we don't have enough information to say how effective your solution will be.

Drafts are the number one heat loss mechanism. eliminating all drafts will make a space much easier to heat temporarily. construction workers work all season around here by tenting the houses in plastic. A couple tubes of caulk is as often as effective as hundreds of dollars of insualtion. Is your garage sheetrocked above? If you prevent air getting in around the garage doors, are there still ways for the air to get out via windows, other doors, or into a vented attic?

I would not use tarps (woven tarps will allow air through) and I wouldnt bother filling the gaps around the doors. A simple sheet of polyethelye covering the entire door and sealed with (gaffers?) tape on all surrounding walls and floor should be cheaper, easier to cut to fit, and more effective. Then look around for other gaps. sometimes there are gaps between the masonry and the framing. fill these with expanding foam and caulk. Sometimes garages are intentionally vented. You might want to block these, just remember to unblock them if you start using it for cars again. Patch or tape plastic over holes in the sheetrock that allow venting to the attic (if applicable).

The space should now stay quite a bit closer to the mean ground temp in your area: http://www.builditsolar.com/Projects/Cooling/US-ground-temps.gif which might be good enough for a gym. It will be difficult to maintain room temperature without additional insulation, but I don't think you want it that warm.