This article reports the results of an experimental study, where a vertical aluminum plate embedded with a heater standing in quiescent air is considered. The temperature time history of the plate for the three stages of the experiment, namely (i) heating, (ii) steady state, and (iii) cooling, has been obtained. Using the temperature time history from heating and cooling, a crucial thermal property of the surface of the plate, namely emissivity together with the heat transfer coefficient from the plate under natural convection, is estimated. The parameter estimation is done through the stochastic-based Bayesian inference method, by posing the inverse problem as a minimization problem, wherein the sum of the squares of the difference between the measured temperature time history and numerically generated temperature time history with guess values of the parameters is minimized. Experiments have been done for (i) a plate with black coating, (ii) a plate with aluminum coating, and (iii) a polished plate. The novelty in the work is the simultaneous estimation of the two properties without the need for vacuum, and the results compare favorably with benchmarks in the literature. Finally, the results from the steady state are also obtained for validating the estimates obtained from transient experiments. The Bayesian method allows the simultaneous estimation of the standard deviation of the estimates.