What are some abiotic changes that might occur if the temperature of the tundra increased. The exact temperature doesn't matter, just enough to change the tundra.

Warmer temperatures would lengthen the growing season; therefore, the trees and other plants would grow taller. However, this may not be an abiotic change. But increased temperature surely would result in a different humidity and probably in more rain. That, in turn, could lead to more leaching, more run-off, more erosion, etc. I hope this addresses your question properly.