In this work we investigate by computational means the behavior of two orthologous bacterial proteins, a mesophilic and a thermophilic tetrameric malate dehydrogenase (MalDH), at different temperatures. Namely, we quantify how protein mechanical rigidity at different length- and time-scales correlates to protein thermophilicity as commonly believed. In particular by using a clustering analysis strategy to explore the conformational space of the folded proteins, we show that at ambient conditions and at the molecular length-scale the thermophilic variant is indeed more rigid that the mesophilic one. This rigidification is the result of more efficient inter-domain interactions, the strength of which is further quantified via ad hoc free energy calculations. When considered isolated, the thermophilic domain is indeed more flexible than the respective mesophilic one. Upon oligomerization, the induced stiffening of the thermophilic protein propagates from the interface to the active site where the loop, controlling the access to the catalytic pocket, anchors down via an extended network of ion-pairs. On the contrary in the mesophilic tetramer the loop is highly mobile. Simulations at high temperature, could not re-activate the mobility of the loop in the thermophile. This finding opens questions on the similarities of the binding processes for these two homologues at their optimal working temperature and suggests for the thermophilic variant a possible cooperative role of cofactor/substrate.