We present a new approach to simulating unsteady heat transfer, with only very few degrees of freedom, by employing directly eigenmodes extracted from DPIV/DPIT experimental data. In particular, we formulate Galerkin low-dimensional systems of the coupled Navier-Stokes and energy equations using hierarchical empirical eigenfunctions extracted from an ensemble of velocity and temperature snapshots. We demonstrate that even severely truncated Galerkin representations (two velocity modes and four temperature modes) produce simulations capable of capturing the dynamics of the flow and heat transfer. This finding is documented by applying proper orthogonal decomposition to water flow past a heated circular cylinder at Reynolds number 610.