You are correct that different colored LEDs generate different amounts of heat, but perhaps not for the reason you might expect.

Heat in most cases is generated through inefficient energy conversion. Most of the heat comes not from the color of light itself, but from the inefficiency of the device making the light. In LEDs, this inefficiency is generally because of defects in the materials, and scientists are continuing to improve these materials and their performance.

As with anything, devices also tend to generate more heat when they produce high intensity light. For a given color, a brighter LED will generate more heat because more electrical current is passing through the device, and any inefficiency will become obvious.