In this study, an inverse heat transfer problem of parameter estimation using Bayesian inference is considered. Single parameter (specific heat of solid material) estimation as well as simultaneous estimation of two parameters (specific heat and emissivity) is done using a methodology combining the Bayesian inference with Markov chain Monte Carlo (MCMC) based sampling method. Computation of posterior probability density function (PPDF), using Bayes formula, is central to the inverse determination of parameters using Bayesian inference approach. Maximum-a-posteriori (MAP) and posterior mean are used to report the values of the estimated parameters and the uncertainties in the estimated parameters are characterized by the variance of the PPDF. The estimated value of specific heat and emissivity is well in agreement with reported value in literature.