We investigate signatures of topological quantum phase transitions (TQPTs) between the Z(2) quantum spin liquids (QSLs). In two spatial dimensions, Z(2) QSLs and their TQPTs are only well defined at zero temperature (T = 0), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between Z(2) QSLs with Majorana fermions in terms of thermal Hall conductivity kappa(xy) at nonzero temperatures. The kappa(xy)/T shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near T = 0 and the peak of kappa(xy)/T around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions fording TQPTs between the phases with different Chem numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in alpha-RuCl3.