This is the method I was thinking of. In fact, I worked out an equation just to verify that it would work:

x = (Ta - Tm) / (Ta - Tb)

where:

x = percentage of total water that is boiled

Ta = temperature of ambient water

Tm = desired temp of mash (actually of strike water)

Tb = temperature of boiling water (212 °F at sea level)

example:

Ta = 60 °F, Tm = 166 °F, Tb = 212 °F

x = .697, so 69.7% of the total water amount would be boiled, the rest would be at ambient temperature.

checking:

.697 * 212 + .303 * 60 = 165.9 °F

Of course, medieval brewers knew nothing about algebra and only knew the ambient temperature in general terms (cold, really cold, not so cold, kinda warm, etc.) but with trial and error and learning from the work of others, they could brew consistently.

...OK, so i was bored last night