We consider a system of two coupled particles fluctuating between two states, with different interparticle interaction potentials and particle friction coefficients. An external action drives the interstate transitions that induces reciprocating motion along the internal coordinate x (the interparticle distance). The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. We focus on how the law of interaction between the particles affects the dimer transport and, in particular, the role of thermal noise in the motion inducing mechanism. It is argued that if the interaction potential behaves at large distances as x(α), depending on the value of the exponent α, the thermal noise plays a constructive (α > 2), neutral (α = 2), or destructive (α < 2) role. In the case of α = 1, corresponding piecewise linear potential profiles, an exact solution is obtained and discussed in detail.