I’ve has melasma for several years and heat becomes a major activator in the summer and I’m not sure how to get past it.

Thanks for your question. Melasma is a difficult condition that we are learning more and more about all the time. There are many factors that seem to contribute such as UV light, visible light, inflammation, and hormones. When we look at treatment all these factors need to be considered, it is often the light that is one of the biggest contributors so strict adherence with sunscreen that has zinc or titanium to protect you from UV light as well as iron oxide to help with visible light and an antioxidant serum is extremely important in managing anybody’s melasma. Reapplication of sunscreen is very important, a product I find many women like is Colorscience as this is in a makeup style brush and can be put on right over makeup and offers high SPF with protection from UV and visible light sources. Other agents I often use are hydroquinone, Heliocare (an oral supplement that as UV protective benefits), other non-hydroquinone lightening agents, and a newer agent to be used in the US is tranexamic acid. As you note with the area the brim of your hat rubs there is also an inflammatory component to melasma so controlling friction is important in your case as well. 
For many people birth control can contribute to their melasma but it isn’t always a fix to change types or even be off of the medicine. This is something you should discuss with the person managing your birth control but probably worth a trial of a different option.
After you have addressed the things you are able to that we know contribute to melasma then there are different treatment/procedural options that work quite well to help with the pigmentation. The options are wide, largely because none of them work perfectly for every person. Some of these options include chemical peels such as the modified jessner, microneedling, PRP, and different types of laser (ensure the person doing the laser understands melasma as many lasers can worsen melasma).
So in the end there are many other options to try but there isn’t a one size fits all answer. I would suggest you see a board certified dermatologist in your area. Good luck.

We have amazing results with the Picoway laser for melasma.  Melasma can be worsened by your hormones so if you could come off the pill this may help.  I would recommend a sunblock like ELTA everyday.  As well, try to avoid sun as much as possible.  Consider a lightening cream as well for daily use such as hydroquinone ( beware the side effects) kojic acid or something of the sorts.