What role might an abiotic factor such as temperature play in the evolution of a species?

Temperature can fall in as one of the factor in evolution. A temperature deflection can create natural selection that demands individuals that are better adapted to the new temperature to thrive/survive, causing the remaining population to die or disappear.

This applies in different forms. Most living organisms are killed by high temperature; at low temperatures, they become inactive; and at optimum temperatures for metabolic activities they grow and reproduce rapidly. Many organisms living in temperate and arctic regions show adaptions that allow that allow them to live at low temperatures.