Many economic sectors, like housing or transportation, are exposed to climate and likely to suffer efficiency losses when climate changes. The global economy is far from dematerialized yet, these sectors represent a significant fraction of the existing capital stock. Using an optimal growth model with perfect knowledge, we examine the balance between these efficiency losses and investment in adaptation measures, which can become sunk costs when climate changes even more. Simulations remind that adaptation should be proactive rather than reactive: protection measures installed today are not designed for today's climate only, but anticipate future warmer conditions over their lifetime. While there is an over-investment compared with a no climate change baseline, the overall cost to adapt is relatively low in front of the potential losses from misadaptation. This allows to stay almost always well adapted to climate.