The issue of greenhouse gas (GHG) stabilization stands on three critical open questions. Namely, what are the impacts deriving from different levels of climate change and their distribution. What are the levels at which GHG concentration should be stabilized in order to avoid unacceptable impacts. And, finally, what are the costs and what are the instruments available to reach such stabilization targets. In the present paper, we address the latter question, in the specific attempt of shedding some light on the debated role of technological progress in lowering the costs of GHG stabilization. In particular, we use an optimal growth climate-economy model, where technical change is endogenously driven by learning by researching and learning by doing. In the model, when an ambitious stabilization target has to be reached, some additional technological innovation and diffusion is induced. The magnitude of this induced effect substantially affects the costs of stabilizing greenhouse gasses and may even make a well-designed climate policy a win-win strategy. A sensitivity analysis on the model crucial parameters is performed to account for structural and parametric uncertainties on learning effects, on the relationship between knowledge accumulation and the energy and carbon intensity of the economic system, and on the crowding out of investments in the energy sector R&D with respect to other research fields.