Two major problems in the study of curvature invariants for curved quantum tori consists of: extending curvature computations to higher dimensions in a uniform manner, and computing curvature invariants for non-conformally flat geometries. Both problems need new ideas. In this talk I will first discuss both problems and then I shall present a solution to both problems under some restrictions on the nature of the metrics on higher quantum tori. We introduce an extension of conformally metrics, called functional metrics and associate a Laplace type operator to these metrics. We show that the first two terms of the heat trace for these metrics can be computed in a uniform manner in all dimensions resulting in universal formulas for scalar curvature. Based on joint work with Asghar Ghorbanpour (available in arXiv).