I'm seriously considering removing the tar on the bottom side of the car - if only to check the condition of what's underneath. I assume a heat gun should do the trick unless I can find a cheap source of dry ice (local welding shop had some a few years ago I recall).
Warren-I remember you did this with your car. How much weight would you estimate comes off the bottom in all?

 

I just removed most of it and I do not recommend heating it. Fumes are pure poison, so mechanical approach is the way to go. I hooded up, put on mask and goggles and used angle grinder with wire wheel.
Some areas I hit with small sand blaster, but most came off with wire wheel and hand scraper, with hammer.

 

I started with the angle grinder and wire wheel, but after removing some skin from my chest I did some experimentation with a heat gun and paint scraper I found the easiest way was to grind a half moon on a 2" paint scraper and go at it cold. This way it removed back to bare metal, it is tough going and I scored a few blisters.

It was way less messy than the wire wheel and did a better job of taking the tar off. Using the heat gun takes the tar off easily and leaves the paint behind, I have taken the underneath back to bare metal and cold was definitely better for this.

 

The later Jags used galvanised metal so grinding would also remove this. Not convinced this is a good idea from a rust prevention point of view!
Heat and scrape or chemical paint stripper and scrape would be my prefernce, Use appropriate safety gear.

 

I did not remove all to bare metal, some areas I only ground down to thinner tar coat and re-coated. I did clean important areas, like seams and corners to bare paint and metal. In my case, I have nothing to save, with 1982 paint underneath, so recoating with self etching primer, paint and Truck Bed coating was the way to go for me. Also, do not forget seam sealer, where applicable...