Thanks for the additional information.
Yes, the adhesive on stick-on velcro isn't designed to hold up to the heat of a hot car in summer.
As I mentioned, there are industrial-strength velcro products that are designed to permanently stick to walls and such, but I think those will not release from your leather seat without damaging it!
One thing you could try is "U-Glu", which is one of those "as seen on TV" wonder products: UGlu
It does have good sticking power, especially on something as light as what you're describing, and it can be removed by stretching it (it will probably leave a mark, but wouldn't be expected to tear the leather.)
I'm not 100% sure it will hold up to the heat of the car either, but it's worth a shot.
Another expert suggested trying a silicone temporary adhesive - it should allow you to remove the velcro and silicone as one piece (it is stretchy, like the UGlu product above.)
Anything else I can think of is just not likely to be removable.
The only other ideas I can suggest would be to design some ties for the back support, so that you could tie it over the top of the seat at the headrest, and around the back of the seat.
Or, design a pillow case like top to the back support, so that it could be slipped over the seat back and stay in place that way.
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Edited by MJ on 8/18/2010 at 9:30 PM EST