One article confirmed very interesting findings. A beard fully hydrates after only 2-1/2 to 3 minutes in 120• water; later in the experiment, we find that cold water doesn't hydrate beard fibers as quickly as warm water - though we don't find out how much more quickly.
Strictly speaking, it uses a solution of SLS, and the time you're asking for is secondary on the chart, but you might want the spot where the curve starts to bottom out.
I found Stereoimaging Of Trapped Hairs very worthwhile, too. The science part may be a little squishy, but it convinced me that trapped hairs are an important factor in shave quality.