also, you don't need a locker to dry clothes in the "locker room"
where I work, we have the standard Euro concrete block buildings with these types of Euro radiators. on every radiator shirts and clothes are drying from commuters, towels and everything else. in fact, i just use what ever body wash bottle is kicking around close to the shower, enevr bring my own (but, I do bring my own towel, which i hang on the radiator in the office).
you could just leave your sweaty clothes drying in the locker room and they'd be there when you got back and if they were gone (they were cheap, right?) just ride home in the work clothes.