Guided by the recent experimental finding of the key role played by the ion heat channel in the transition from low (L) to high (H) confinement mode (Ryter et al 2014 Nucl. Fusion 54083003, Schmidtmayr et al 2018 Nucl. Fusion 58 056003), the present phenomenological model of the power threshold for the L-H transition is developed by combining the energy equipartition between electrons and ions, and the L-mode scaling of the energy confinement time. This heuristic model describes with continuity the transition of the power threshold from the low- to the high-density branches and clarifies the origin of the main dependence of the power threshold on the plasma current in the low density branch.