Could a large burst of super-heated or super-cooled air cause tornadoes to fall apart?
Changing air currents is very difficult and energy intensive.  You'd need to alter an entire weather system - no easy feat.  If you heated a very large region of cool air you might prevent the spiraling that causes tornadoes to form, but you'd need to warm at least few states worth of upper atmosphere.   It would be an enormous undertaking.   

There's also the logistical problem of how would you go about doing it?   Heating in principal can be done faster than cooling, presumably sending up a whole lot of hydrogen in a few hundred balloons and igniting it forming hot water-vapor, which as it condenses, would further heat the atmosphere.    Cooling warm air is harder as there's no quick and easy method to cool an enormous  volume of air, so I think heating the high cold air would be easier than cooling the low moist air, but it would still be an enormous effort and probably cost more in prevention than the tornadoes are likely to do in total damage.

http://images.slideplayer.com/22/6379142/slides/slide_22.jpg

There's no neat and tidy technological trick to get it done that I can think of.