Beer production does not involve boiling water.

Alpha-Amylase conversion is optimal (for beer production) at about 140 F/60 C. Second and third extractions occur at about 155 and 175 F, respectively, well below the boiling point.

More importantly, the first extraction only marginally reaches pasteurization temperatures (using low-temp long time parameters), so the majority of liquid in beer inhibits, but does not completely kill, pathogens.

If we're talking about medieval beer production, it certainly started with boiling the water.

In absence of temperature measurement, they would time how long the water had been off the boil before it would be used.

They also commonly believed that the boil was integral to the carbonation in the final product. That the amount of time spent boiling the water correlated to more bubbles in the beer, and would often do things like boil the water until it was half gone.