The solution to the boundary integral equation defining undercooling at the surface of a parabolic dendrite growing in an inclined melt flow is obtained. The temperature gradient with respect to dendrite's normal direction and the isotherms in liquid around the dendritic tip are analytically found. We show that the undercooling at dendritic surface responsible for its growth rate can change about 5-7% in the presence of small flow slope. In addition, we show that the isotherms shift towards the incoming melt flow. This theoretically confirms favourable conditions for the growth of secondary patterns in the direction of liquid flow.