The design of computationally efficient model predictive control (MPC) systems for the thermal control of buildings is a challenging task since long prediction horizons may be needed, which can take a significant computational time, especially when multizone buildings are considered. In this paper, we investigate the computational performance of a potential approach for this purpose, Laguerre network-based MPC (LN-MPC), for thermal control of buildings, where parameterization of control input over the prediction horizon is used to reduce the number of decision variables. The computational performance of the suggested framework with comparison to the classical MPC framework is investigated through a detailed case study. It was observed that although LN-MPC can produce almost the same results as the classical MPC with a considerably smaller number of decision variables, it has no computational advantage. The potential reasons behind the lack of improvement in the computational performance of LN-MPC are also discussed.