I was just doing some research this afternoon regarding tread softening (Canyon707 has M/T drag tires getting a little hard, has a thread in the Time Slip forum).
The softening works, usually it's some sort of solvent based product (xylene, toluene, diesel fuel, mineral spirits, acetone, etc) that actually changes the composition of the rubber. From what I can tell, it is actually melting it a bit. If it softens and melts the ashpalt in the street, it will probably soften tires
The fear is catastophic tire failure...it probably won't happen, but then again you could have a total delamination at speed under acceleration. Not a big problem on a dirt track or circle track $4500.00 stock car (and maybe going 60 mph), but a bigger concern is regarding the cost and speeds that a Viper might be hitting.
Be safe,
George