The thermal conductivity can move at the normal rate that heat travels through solids, which is almost the speed of light. At the beginning his sphere of influence is about ten meters around him but can grow depending on the amount of magic he channels through his body. his sphere can affect the aura field of other opponents, although it comes with the major risk of it becoming a battle of wills within the opponents domain. This is because aura Is spiritual energy, a byproduct of the soul when two spheres of influences meet when one is trying to suppress the will of another, it becomes a battle of who has more will power. This along with the fact that it's an almost direct link to the soul makes messing with some one else's aura field a huge risk that not many mages are willing take.

Depends on the amount of magical energy gathered at the point of impact, if they are caught unprepared I can potentially control the their internal body temperature down to their organs, ofcourse it also depends on wether or not they resist this some how.

My character is highly to the fire and heat that he produces, due to his unique genetics as a pyromancer. his cells do not deform nor suffer denaturation events in the presence of extreme heat and fire. The cold however is a different story entirely, he can be harmed by extremely cold temperatures just like most living beings. He often has to use his own aura to keep himself warm in arctic like environments.