I use a multi-sector vintage capital model à la Krusell (1998) with climate economics to study timing of optimal energy transition. I include an exogenous technology differential between renewable and fossil, that will be the engine of growth. The vintage structure is used to modelize embodied technical change and carbon lock-in as it is mentioned in Unruh (2000), a situation in which we are trapped by carbonized energies and by slow transition. Economy being mainly fossil driven, about 82% of the energy mix, it creates inertia in energy capital sector that cannot be solved by technology, in the short run. Because capital unit are long-lived and technology is embodied, energy transition faces frictions to occur quickly. Preliminary results show a slow transition, with a ratio of renewable technologies that should remain below the 20\% level in 2050. The second part of the paper tries (not in this version of the paper) to confront theoretical result to the data using a bayesian vector auto-regressive model (BVAR) on energy capital investments. This part relies on the "power plant tracker" dataset, from Enerdata. Econometric forecast would validate (or not) the theoretical model and measure the importance of capital inertia in the energy transition process.