The article presents the prototype of a measurement system with a hot probe, designed for testing thermal parameters of heat insulation materials. The idea is to determine parameters of thermal insulation materials using a hot probe with an auxiliary thermometer and a trained artificial neural network. The network is trained on data extracted from a nonstationary two-dimensional model of heat conduction inside a sample of material with the hot probe and the auxiliary thermometer. The significant heat capacity of the probe handle is taken into account in the model. The finite element method (FEM) is applied to solve the system of partial differential equations describing the model. An artificial neural network (ANN) is used to estimate coefficients of the inverse heat conduction problem for a solid. The network determines values of the effective thermal conductivity and effective thermal diffusivity on the basis of temperature responses of the hot probe and the auxiliary thermometer. All calculations, like FEM, training and testing processes, were conducted in the MATLAB environment. Experimental results are also presented. The proposed measurement system for parameter testing is suitable for temporary measurements in a building site or factory.