One other point to remember, putting a lid on the boiler, even partial, does not reduce the heat loading, although it may reduce the 'evaporation' though condensation and dripping back into the wort.
It is thermal loading that is important, and the only way we have to measure this is via open boiler evaporation rates. Incidentally it has been reported that an evaporation of > 20% develops the melanoidins traditionally associated with decoction mashing, even if it was a single tempt infusion mashed beer, and an evaporation rate of <10% produces a beer with a less malty profile . . .even it it was decoction mashed!