Purpose - The purpose of this paper is to study the partitioned solution procedure for thermomechanical coupling, where each sub-problem is solved by a separate time integration scheme. Design/methodology/approach - In particular, the solution which guarantees that the coupling condition will preserve the stability of computations for the coupled problem is studied. The consideration is further generalized for the case where each sub-problem will possess its particular time scale which requires different time step to be selected for each sub-problem. Findings - Several numerical simulations are presented to illustrate very satisfying performance of the proposed solution procedure and confirm the theoretical speed-up of computations which follow from the adequate choice of the time step for each sub-problem. Originality/value - The paper confirms that one can make the most appropriate selection of the time step and carry out the separate computations for each sub-problem, and then enforce the coupling which will preserve the stability of computations with such an operator split procedure.