Do blood vessels increase in size to lose heat?

No, blood vessels decrease in size to lose heat.

When the body needs to lose heat, the blood vessels near the skin's surface dilate (widen) to allow more blood to flow near the skin. This allows heat from the body to escape more easily into the surrounding environment. Conversely, when the body needs to conserve heat, the blood vessels near the skin's surface constrict (narrow) to reduce heat loss.