Your veins are part of the system which controls your body temperature (homeostasis). One of the ways that the veins help to do this is by radiating heat away from the body when your temperature rises above a certain level and limiting the heat loss when your temperature goes down. They do that by dilating and contracting.
In hot weather, the veins just under the skin dilate (enlarge). The veins in your arms and in your legs become very prominent or swollen. The blood flowing through them releases heat through the skin and that helps you to lose heat and keep your temperature down. In people with varicose veins, the already large veins stretch up even more and fill with blood causing some swelling and the feeling of “fullness” in the legs. They are then likely to ache more.
One way to limit the discomfort is to elevate the legs and allow the blood to drain out of the legs, thereby decreasing the swelling. Another way is to use compression stockings to limit the degree to which the veins fill with blood. A similar thing happens when you have a shower. The heat from the water, with the increased hydrostatic pressure from standing, stretch the veins even more, so that the legs begin to swell more. This effect is aggravated further if you have varicose veins.
Note that the NICE guidelines (https://www.nice.org.uk/guidance/cg168/chapter/1-Recommendations#assessment-and-treatment-in-a-vascular-service-2) do not recommend stockings in the management of varicose veins unless endovenous management (such as laser or radiofrequency) is not possible.