In this work, we present an accelerated Bayesian inference approach using polynomial chaos expansion to solve inverse heat conduction problem in a disc brake system. As a demonstration of the approach, we estimate a time-varying heat flux based on transient temperature measurements at a certain location at fixed time intervals on the disc. We represent the flux function using model parameters in the form of stochastic input and compute posterior probability distribution of the heat flux using the temperature measurements. The predicted value of the flux is obtained by computing the expectation of the distribution to obtain the predicted value of the flux and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy. We also study the utility of the technique for higher dimensions by increasing the dimension of the flux function. The results show accurate estimation of the time-dependent heat flux obtained using the given approach.