Topology optimization is widely used to design heat exchangers and may involve different expressions of objective functions to increase heat exchange. This work proposes a new thermal objective function based on the local orientation of velocity and temperature gradient fields. The latter is then defined as the cosine of these two vector fields and thus our approach has connections with the field synergy principle. The cosine objective function is compared with a more classical one in a multi-objective optimization framework whose resolution is done with the adjoint method. Our results reveal that the cosine objective function lead to results that are comparable with those obtained with the classical cost function and may be used by designers to look for optimized design by taking into account the synergy of the fields. A study of the field synergy principle reveals that it is only an accurate indicator of heat exchange in some cases discussed in this article.