Rotation influences flows and transport processes in many engineering applications, however, even in canonical flow cases, the effects of rotation are not fully understood. Here, we present the results of di-rect numerical simulations of heat transfer plane Couette and Taylor-Couette flows subject to rotation about the spanwise and axial axis, respectively. Temperature is a passive scalar since buoyancy is ne-glected. The Reynolds number Re and the rotation rate Rn are systematically varied to thoroughly inves-tigate the influence of rotation on heat and momentum transfer and the Reynolds analogy. We find that with increasing anti-cyclonic rotation, the Nusselt numbers for the momentum transfer Num and heat transfer Nuh both increase at first before declining and approaching unity at rapid rotation rates when the flow becomes fully laminar. The Reynolds analogy factor RA = N uh/N um is near unity for non-rotating Couette flows, but it grows significantly with increasing rotation rate. RA reaches a maximum of approx-imately 2 at low Re up to 6 and 8 near Rn = 1 at higher Re in plane Couette and Taylor-Couette flow, respectively. The simulations thus show that the Reynolds analogy between heat and momentum trans-fer breaks down and that the heat transfer can become much faster than moment transfer when plane Couette and Taylor-Couette flows are subject to anti-cyclonic rotation. This happens at low Re as well as higher Re when the flows are fully turbulent. The turbulent Prandtl becomes much smaller than unity and the mean velocity and temperature profiles differ when the Reynolds analogy breaks down. We also present empirical models for Num and RA , which agree reasonably well to very well with the data within a limited Rn range.