We present a Bayesian estimation framework for the analysis of data from ill-controlled experiments and apply it to the determination of model parameters for heat transfer in a packed bed. The Bayesian method is a statistical procedure that allows the systematic incorporation and proper weighting of experimental data, prior knowledge of model and parameters, and probabilistic models of sources of experimental error. The interplay of these elements determines the best model parameter estimates. Furthermore, because of its probabilistic structure, the method also characterizes uncertainty of the estimates in a natural way. For our heat transfer problem, standard estimation techniques-were not adequate because they did not account for several important error sources. Our analysis explicitly accounts for three major experimental difficulties : (i) standard measurement error of thermocouples, (ii) uncertainty in thermocouple (probe) positions, an error which is sensitive to temperature gradients, and (iii) an uncontrolled inlet temperature profile. This third error source introduces correlations between errors at different probes, and is modeled by solving a partial differential equation with a stochastic boundary condition. The results of this study show the benefits of the Bayesian method in obtaining best parameter estimates with narrow confidence regions. The methodology is quite general and can be applied to the systematic solution of difficult estimation problems in many fields, when sources of uncertainty can be identified and modeled.