In this paper, a comparison of three alternative estimation approaches for a vehicle combustion heating system is presented: 1) a Luenberger observer, 2) a reduced-order observer, and 3) a discrete-time Kalman filter. The estimated temperatures (representing state variables) and unknown disturbance heat flows are employed within a model-predictive on-off control structure. The observer design as well as the model-predictive on-off control are based on a control-oriented model of a combustion heating system, that is frequently installed in road vehicles like buses, cars, and trucks. To evaluate the alternative estimation strategies, the root-mean-square error between the measured and estimated states, the sensitivity w.r.t. noise, and the computational effort are considered. The advantages and disadvantages of each estimation strategy are discussed based on both simulations and experimental results obtained from a dedicated test rig.