A new “rotational” energy flux is derived for highly collisional impurity ions in tokamaks with strong unbalanced neutral beam injection (NBI). The derivation is based on a consistent ordering of kinetic theory. The rotational flux, which is of a collisional origin and vanishes when the rotation vanishes, is ∼ε2δ−1 times larger than the conventional neoclassical energy flux. This rotational energy flux and a previously derived momentum flux of a similar nature reproduce the experimentally observed relation between momentum and ion energy transport, τφ/τi ∼ O(1), χφ/χi ∼ O(1). The magnitude of χi resulting from this rotational energy flux is the same as is observed in many tokamaks with strong unbalanced NBI. This suggests the control of energy confinement via the control of impurity content in strongly rotating tokamak plasmas.