In this article, we apply a Bayesian approach for the simultaneous identification of volumetric heat capacity, thermal conductivity, and boundary heat flux, in a one-dimensional nonlinear heat conduction problem. The Markov chain Monte Carlo sampling approach, implemented in the form of the Metropolis-Hastings algorithm, was used for the solution of the inverse problem. Simulated temperature measurements were used in the inverse analysis in order to examine the accuracy and stability of the overall approach. Independent measurement data were used to construct the prior model for the coefficients to be estimated. The approach is also applied to experiments involving the heating of a reference material with an oxyacetylene torch.