The laser flash method is highly regarded due to its applicability to a wide temperature range, from cryogenic temperatures to the melting point of refractory metals, and to extreme environments involving radioactive or hazardous materials. Although instruments implementing this method are mostly produced on a commercial basis by major manufacturers, there is always room for improvement both in terms of experimental methods and data treatment procedures. The measurement noise, either due to the detector performance or electromagnetic interferences, presents a significant problem when accurate determination of thermal properties is desired. Noise resilience of the laser flash method is rarely mentioned in published literature; there are currently no data treatment procedures which could guarantee adequate performance under any operating conditions. In this paper, a computational framework combining finite-difference solutions of the heat conduction problem with nonlinear optimization techniques based on the use of quasi-Newton direction search and stochastic linear search with the Wolfe conditions is presented. The application of this framework to data with varying level of noise is considered. Finally, cross-verification and validation using an external standard, a commercial and an in-house built laser flash instrument are presented. The open-source software implementing the described computational method is benchmarked against its industrial counterpart.