Computations have been conducted for the case where one rotating disc is heated and the other surfaces are adiabatic. Discs rotating at different speeds are found in the internal cooling-air systems of engines, and it is convenient to define Γ as the ratio of the angular speed of the slower (adiabatic) disc to that of the faster (heated) disc. A finite-volume, axisymmetric, elliptic, multigrid solver, employing a low-Reynolds-number k-ε turbulence model, previously used for a complementary study of the flow structure, has been validated using available heat transfer measurements for Γ = -1, 0 and +1. The effect of Γ (for the range -1 ≤ Γ ≤ +1) on heat transfer is then considered for a generic case in which the rotational Reynolds number, Reφ, is 1.25 × 106. (Although this is much lower than the values found in practice, the magnitude of the coolant flow rate was chosen to produce an engine-representative flow structure). Theoretical values of the adiabatic-disc temperature are in reasonable agreement with computed values for Γ > 0. In the source region, at the smaller radii, there is no effect of Γ on the local Nusselt numbers, Nu, which are consistent with a freedisc correlation. For the average Nusselt numbers, Nuav, the Reynolds analogy shows that the ratio of Nu av/ReφCm, where Cm is the moment coefficient, should be equal to a constant value of 0.259. For Γ ≥ 0, the computed value of this "constant" is within 7% of the theoretical value.