The brake fluid will not, or at least should not heat up on it's own. There is an initial locking, sticking, dragging condition that has to generate heat in the components. Even if it's something like the booster bad internally causing it to hold pressure when it shouldn't ( I have seen it happen on another aftermarket disk brake conversion) and dragging the brakes.
Maybe the lines being too close to the headers is causing it, if that were true, running it for a little bit on stands would yield some results. In over 20 years of automotive experience, more than a decade professionally, through all the manufacturers trainings I have been certified in, including brakes, no one ever told me that there is always "xyz" fix for "abc" problem. I'm not saying I know everything, or that I've seen everything, because I dont and I haven't. All I'm saying is having all the information possible, and doing as much diagnosis as possible, will yield the best results 99% of the time.
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correct.. brake fluid will not heat up on its own...
but driving in traffic or short stop and go conditions for example..
calipers start to warm up.. as warming up ,fluid starts to expand some..
thats normal and excess flows back into bowl when releasing brake..
just getting buy headers alone will not cause dragging brakes, since expanding fluids can still flow back into bowl..and pistons retract..
blocked lines..deteriorating old lines etc..miss adjusted booster rod and so on...causing blockage etc..
with fluids having no where to go.. the more the brakes drag the hotter fluid in caliper get and expand..the tighter the brakes apply/drag....
being a disc brake conversion , a lot is pointing to booster and master cylinder... miss adjustment/miss match..
some troubleshooting and fixes should get him back on the road again..