Parallel tempering molecular dynamics simulation, also known as temperature replica exchange simulation, is a popular enhanced sampling method used to study biomolecular systems. This method makes it possible to calculate the free energy differences between states of the system for a series of temperatures. We developed a method to easily calculate errors (standard errors or confidence intervals) of these predictions using a modified version of our recently introduced JumpCount method. The number of transitions between states (e.g. protein folding events) is counted for each temperature. This number of transitions, together with the temperature, fully determines the value of standard error or the confidence interval of the free energy difference. We also address the issue of convergence in the situation where all replicas start from one state by developing an estimator of the equilibrium constant from simulations that are not fully equilibrated. The prerequisite of the method is the Markovianity of the process studied.