Last time I had a problem like this was on my GSX-R, sticking pistons in the caliper and had the same effect, rode it for a while then started to heat up to a point where you could feel the brake on all the time and having to stop and let it cool down.
Not sure about the newer models but I know one of the things with the earlier Fazers was good maintenance as the rear caliper could seize.
Be worth just dropping the rear caliper off and having a look it's only 5 minutes just to have a look see if there is any damage/road crud to the piston I just done mine without draining any fluid and cleaned up round the pistons as there had been a build up of brake dust and general weather.
Funny you mention the jet wash, I never used one of them but I had problems after a good wash down and scrubbing all round the caliper with a long bristle tyre brush so must have made the dust and stuff go harder.
If it was anything drastic like the piston/s needing replacing if you live in the UK
Wemoto do the pistons and seals and quite a reasonable price, can buy them as a kit.