In this paper, a control-oriented model of a combustion-heating system for vehicles such as buses, coaches and trucks is developed. Based on this model, a novel model-predictive on-off strategy is proposed for the control of the combustion-heating system. Experiments are carried out to obtain a fair comparison of the predictive on-off controller with a classical on-off controller. The classical on-off controller and the predictive on-off controller are evaluated with respect to fuel economy, reduction in the emission of pollutants and the number of on-off switching cycles of the combustion valve connected to the heater. A discrete-time Extended Kalman Filter is employed for the estimation of state variables, heat losses and the volumetric flow. Experimental results show that the predictive on-off control strategy leads to a superior performance in terms of fuel economy and switching action of the valve as compared to the classical on-off controller.