We present a mathematical method based on Laplace transform techniques for the analysis of heat capacity and thermal conductivity measurements, for the case of thin film samples on substrates of finite lengths. The method is a further development of the heat pulse technique. This mathematical analysis is capable of separating the heat capacity and thermal conductivity of the sample from those of the substrate, thus eliminating the need for an additional measurement on the substrate alone. This fact substantially reduces the errors and complexity of the experiment and also makes the heat pulse technique the only one capable of obtaining thermal parameters on thin films in a single experiment. The analysis of the experimental data is performed by calculating several moments of the temperature rise in two thermometers as a function of time. Special considerations are taken to adapt the method for on-line computer experiments.