This thesis seeks two objectives. One objective is to develop a means to estimate time invariant real contact areas and surface temperatures through thermal measurements in 1D/2D systems. This allows computationally easier models, resulting in faster simulations within acceptable convergence. The second objective is to provide experimental design guidance. The methods used are a modified cellular automata technique for the direct model and a Levenberg-Marquardt parameter estimation technique to stabilize inverse solutions. The modified cellular automata technique enables each piece of physics to be solved independently over a short time step, thus frequently allowing analytical solutions to those pieces. Overall, the method was successful. The major results indicate that appropriately selected measurement locations can determine the contact distribution accurately, and that the preferred measurement location of the sensor is not very sensitive to the contact distribution specifics. This is useful because it allows selection of measurement locations regardless of the specifics of the generally unknown contact distribution. Further results show the combined effects of the normalized length and the Stanton number have a significant impact on the estimation quality, and can change the acceptable sensor domain, if the loss is high. The effect of placing the sensor in the static body can, for low loss, provide a coarse image of the contact distribution. This is useful because the static body is easier to instrument than a moving body. Finally, the estimation method worked well for the most complex model utilized, even in a sub-optimal measurement location. / Master of Science