In this article we study the finite temperature and chemical potential effects in a nonlocal Nambu-Jona-Lasinio model in the real time formalism. We make the usual Wick rotation to get from imaginary to real time formalism. In doing so, we need to define our regulator in the complex plane q(2). This definition will be crucial in our later analysis. We study the poles in the propagator of this model and conclude that only some of them are of interest to us. Once we have a well-defined model in a real time formalism, we look at the chiral condensate to find the temperature at which chiral symmetry restoration will occur. We find a second-order phase transition that turns to a first-order one for high enough values of the chemical potential.