All the DIY LPMs are using a TEC based sensor. The smaller the Peltier TEC, the shorter the reaction time for the meter. Something on the order of 15X 15 mm or 10X 10 mm will work fine as long as you can use one with a high enough pn density. The fewer pn junctions in your sensor, the less accurate and precise it will be.
You're welcome. After you get the TEC, you will need to coat the surface of the side opposite to the side with printing on it with a black, non-reflective paint and a carbon, such as graphite to absorb the light as opposed to reflecting it. The side that needs to be coated is only from my limited experience with the TECs I've used. The easiest way is to connect your voltmeter across the leads: positive to red and negative to black and see what the polarity of the voltage across the TEC is when you focus the beam from a laser at the surface.
The output voltage would be lower, but not less linearly proportional to the amount of heat transported. It could be a problem to read a very low voltage with a given DAC, but then again you could easily amplify the signal with an opamp to fit the input range of the DAC.
Speed is a real factor here, you don't want to wait a minute to get a good reading. A small TEC will help with this, provided it can handle the laser power without damage.
To some degree it's possible to do some calculations in software to estimate power while temperatures still rise so you don't have to wait for the equilibirium to get a ball park figure.
My understanding is that the more pn junctions one has the better the voltage measurement will be along the entire curve that the heat is measured. I also know if you don't have enough, it will not produce enough voltage to measure without additional noise in the reading, so if you amplify it, there will be a S/N ratio degradation. The reason the 10X10mm wouldn't work for his project was because the output voltage was too small.