Mathematical modelling is the theoretically established tool to investigate and develop solar thermal collectors as environmentally friendly technological heat producers. In the present paper, the recent and accurate multiple linear regression (MLR) based collector model in Ref. [1] is empirically improved to minimize the modelling error. Two new, improved models called IMLR model and MPR model (where MPR is the abbreviation of multiple polynomial regression) are validated and compared with the former model (MLR model) based on measured data of a real collector field. The IMLR and the MPR models are significantly more precise while retaining simple usability and low computational demand. Many attempts to decrease the modelling error further show that the gained precision of the IMLR model cannot be significantly improved any more if the regression functions are linear in terms of the input variables. In the MPR model, some of the regression functions are nonlinear (polynomial) in terms of the input variables. (C) 2016 Elsevier Ltd. All rights reserved.