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Thermogenesis results from the cellular metabolism and has a fundamental role for body thermoregulation in endothermic species. The motivation for this work is the analysis of the kidneys' contribution for thermoregulation. An inverse problem is solved for the estimation of the heat generation rate that results from the metabolic activities in the kidney, by using transient temperature measurements of the urine. The Markov chain Monte Carlo (MCMC) method is applied for the solution of the inverse problem, which presents inherent difficulties associated with low sensitivity of the parameters of main interest that represent the transient heat source term and strong correlation of the remaining model parameters. Such difficulties are dealt with in this work by using a version of the Metropolis-Hastings algorithm that samples the parameters in blocks. Simulated temperature measurements are used for the inverse problem solution, and the convergence of the Markov chains is verified with two different techniques., (© 2019 John Wiley & Sons, Ltd.)