High temperature air rises (by expanding and becoming less dense), the void is filled with low temperature air. So a colder forest will start a wind outward of

High temperature air rises (by expanding and becoming less dense), the void is filled with low temperature air. So a colder forest will start a wind outward of the forest towards the warmer areas, thereby distributing the colder air into the surrounding area. You can see the same effect mostly in spring in coastal areas, when the land is heated faster than the sea. Hot air over land will rise, colder air from the sea will move in, causing thermal wind, making the coast a lot cooler. This can cause enough wind for kitesurfing or wingfoiling.