Except it really depends if Rukia can take away energy fascompound at 500 C and if they are in the same state they will reach an equilibrium at some temperature between the two depending on Cp values and what not. Same idea applies is that if an absolute 0 touches yamas flame they heat up to an equilibrium so it really becomes who takes away/puts in energy faster. Tikis is essentially removing energy faster than the environment puts it in, doesn't mean Yama isn't faster. But she does do it quickly because her bankai flash froze everything around her.Logically, Rukia should beat Yamamoto, because she can freeze stuff to Absolute Zero. That's some serious breaking of the laws of thermodynamics.. Absolute Zero means she is removing energy from the system, and so she should be able to remove all the energy in Yamamoto's flames.
Yamamoto ignores Logic, and punches her. Rukia dies.