A while ago, there was a fad to have T-shirts that changed colors with changes in temperature. How did those shirts work?

Those shirts probably used the micro-encapsulated chemical systems that I described as present in the color-changing BIC pens. Tiny chemical bubbles are incorporated in a plastic material that can be used to form toys or household objects or even the writing on T-shirts. Inside each bubble are several chemicals, one of which melts at a temperature very near room temperature. When that chemical melts, it begins to interfere with the other chemicals so that they lose their colors. That way, part of the object's color disappears when it warms up. The plastic contains other normal pigments so that it doesn't become colorless when warm, but it does become more lightly colored.

Why do you sometimes see a circular rainbow surrounding a light?

It is most often caused by the bending of light by mist around the light or by flaws in the optical components through which you are viewing the light. Whenever light passes through a clear material, its path bends. In most cases, you only notice that the light is distorted by its passage through the material. But different colors (wavelengths) of light bend by slightly different amounts so that the colors of light sometimes appear to come from slightly different directions. That's the origin of the rainbow you see.