The energy efficiency of industrial plants is an important matter regarding the goals of a climate-neutral economy by 2050. To increase the energy efficiency of industrial plants, sophisticated controllers that optimise the performance of the plants, with regards to the minimisation of their energy consumption, are considered. Such a control strategy is an explicit solution of model predictive control (MPC) which meets the requirements of the implementation of optimal control along with the ability to be easily applicable in practice as the optimisation problem is not solved in the online phase. This paper proposes the idea of self-tunable approximated explicit MPC. The tuning of approximated explicit model predictive control is performed through linear interpolation between two optimal explicit MPC controllers. The explicit controllers are constructed based on different input penalty matrices - the upper and lower bound on penalty matrix R. A novel idea of self-scaling of penalty matrix R is presented. Based on the distance of the reference value from the steady state, the aggressiveness of the controller is adjusted whenever a change of reference occurs. The proposed idea of this online self-tuning of the explicit controller is applied to a system of a laboratory heat exchanger. As the aggressiveness of the approximated controller is adjusted during control, improvement in control performance is achieved compared to the explicit controllers utilizing the lower and the upper bound on penalty matrix R during the whole control. In addition, the proposed method also leads to decreased energy consumption associated with the volume of the heating medium. After 1 hour of plant operation, the heating medium savings reach 80 ml and the associated energy savings are approximately 2 kJ.