Following the ideas of J.P. Dias and H. Frid we adapt the calculations by Kazhikhov on the 1-d theory of the Navier-Stokes system to show global existence and uniqueness of solutions to the Cauchy problem for a coupling between a Navier Stokes System and a Schrödinger equation, all of this in the one (space) dimensional context. This coupling was proposed by Dias and Frid and therein, after proving local solvability through a Faedo-Galerkin type method, they used a priori estimates to prove the existence of global solutions. They did this for the case of a non heat conductive fluid. We generalize these results to the heat conductive case.