In this paper, we study harmonic maps relative to (alpha )-connections, but not necessarily relative to Levi-Civita connections, on Hessian domains. For the purpose, we review the standard harmonic map and affine harmonic maps, and describe the conditions for harmonicity of maps between level surfaces of a Hessian domain in terms of the parameter (alpha ) and the dimension (n). To illustrate the theory, we describe harmonic maps between the level surfaces of convex cones.