  In this paper we study AdS-Schwarzschild black holes in four and five
dimensions in dRGT minimally coupled to a cloud of strings and investigate the
effects of this string cloud on the thermodynamics of the black holes. It is
observed that the entropy of the string cloud and massive terms does not affect
the black hole entropy. The observations about four dimensions indicate that
the massive term in the presence of external string cloud can not exhibit Van
der Waals like behavior for AdS-Schwarzschild black holes and therefore there
is only the Hawking-Page phase transition. In contrast, in five dimensions, the
graviton mass modifies this behavior through the third massive term, so that a
critical behavior and second order phase transition is deduced. Also, the
Joule-Thomson effect is not observed. The black hole stability conditions are
also studied in four and five dimensions and a critical value for the string
cloud parameter is presented. In five dimensions a degeneracy between states
for extremal black holes is investigated. After studying black holes as
thermodynamic systems, we consider such systems as heat engines, and finally
the efficiency of them is calculated.
