We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange J and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two nearest sites of a simple cubic lattice. We suppose that dimers are self-avoiding and can have only three orientations, which coincide with the x, y or z direction. The interaction J is attractive if the two dimers are parallel to each other at the NN distance, zero otherwise. The truncated dipolar interaction is characterized by two parameters: its amplitude D and the cutoff distance rc. Using the steepest descent method, we determine the ground-state (GS) configuration as functions of D and rc. We then use Monte Carlo simulations to investigate the nature of the low-temperature phase and to determine characteristics of the phase transition from the ordered phase to the disordered phase at high temperatures at a given dimer concentration. We show that as the temperature increases, dimers remain in the compact state and the transition from the low-T compact phase to the disordered phase where dimers occupy the whole space is of second order when D is small, but becomes of first order for large enough D, for both polarized and nonpolarized dimers. This transition has a resemblance to the unfolding polymer transition. The effect of rc is discussed.