We study the finite-temperature nature of a quantum phase transition between an Abelian and a non-Abelian topological phase in an exactly solvable model of the chiral spin liquid of Yao and Kivelson [Phys. Rev. Lett. 99, 247203 (2007)]. As it is exactly solvable, this model can serve as a testbed for developing better measures for describing topological quantum phase transitions. We use the global flux and entanglement entropy to characterize this phase transition, and we discuss to what extent the existence of a topologically ordered ground state with non-Abelian excitations is revealed at finite temperature. © 2010 The American Physical Society.