The paper deals with the design of an experiment for estimating thermophysical parameters in a problem described by Sawaf et al. (1995) and Ruffio et al. (2012). Its aim is to illustrate potential problems connected to the application of a nonlinear regression with "nuisance" random parameters for estimating parameters of interest. Presenting four simplified versions of the problem where a solution is found numerically and its quality is assessed by a Monte Carlo simulations this paper presents typical features of nonlinear regression with random common factors. (C) 2016 Elsevier Ltd. All rights reserved.