Saw the following description of testing laser power from reddit. Original link at the end of this post.
Measure 1g of water, which is a volume of quite exactly 1cm³. Mix the charcoal powder into the water so that you get a nicely opaque density, but it should not absorb all the light right at the surface. Put the thermometer into the water. Then shine the laser into the water (mind the specular reflection). About 4% of the power will be reflected off the surface, the rest gets absorbed by the charcoal, which heats up and dissipates the heat to the water. Measure the time it takes to heat up the water by 10K (=10°C). The heat capacity of water is about 4.2J/(g·K), so to heat up 1g of water by 10K it takes 42J. So if it took your laser t seconds to heat up that beam dump by 10K the power is 42J/t. Now remember that about 4% get reflected and don’t contribute to the heat, so 42J/t = P · 0.96 thus P = 42J/(0.96·t)
Assuming a 1W output power of your laser, if we put the numbers in:
1W = 42J/(0.96·t)
t = 42J/(0.96W) = 43.75s
So it would take a 1W laser about 45 seconds to heat up blackened water by 10K.
Math works out about the same. Wonder if the charcoal really makes any difference…