I have cooked my discs touring, never cooked rims. You need to watch out for steep sections where you need to brake constantly because you can't let speed build up because of the road surface or some other reason. Discs like to be pulsed, dump a heap of heat in quickly, then let it radiate/convect out quickly. Constant energy input will eventually see them fade if the hill is steep or long enough and you are heavily loaded. . Either brake type; use wind resistance to you advantage if you can, sit up before the corner and turn yourself into a parachute then do the braking you need to in a short burst, allowing time for the heat to dissipate before the next corner.
Unfortunately it may reach a stage where it's hard to spec a tourer with rim brakes, as good quality rims with brake tracks are becoming less common.