A heuristic and adaptive model predictive control algorithm is presented in this work which operates domestic refrigerators connected to an electrical grid operating in a day-ahead market (DAM) and temperature constraints also have to be met by the refrigerator temperatures. The problem has been solved using the model predictive framework using a simple refrigerator model. This paper is a continuation of a previous work that has been extended so that the optimal scheduler algorithm adapts its steps to the actual estimated interior heat capacity of the refrigerator (which depends on the food quantity, food temperature, etc. in the interior). It is shown that the proposed adaptive MPC based scheduling algorithm gives a better performance (with respect to price) as opposed to the scheduling algorithm having no precise knowledge of the actual load of the refrigerator. Moreover, due to the adaptive behavior it was possible to decrease the running time of the optimal scheduler algorithm compared to the non-adaptive version.