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We establish existence of travelling fronts in thermo-diffusive systems of the KPP type in a shear flow with an arbitrary Lewis number and a positive heat-loss at the boundary. We then prove that the leftover concentration behind the front is positive, and that it is small when the heat-loss is small. On the other hand, when the heat-loss approaches a critical value, the temperature becomes uniformly small. Finally, in the limit of large flow amplitudes A, we show that, depending on the flowdoi:10.1088/0951-7715/18/6/024 fatcat:5dpdixdlu5czdnw4uise4t6qsa