Kill-A-Watt or similar, probably, since he said the rig (whole rig, not just the CPU) pulls 187w from the wall.
If you unlock your X2 to an X4, then it will have the same TDP as the X4 counterpart.
However, the TDP is not always specific to a processor. The TDP serves as a guideline for the power and cooling needed so that OEM/board makers know how to design and build their line of products. Keeping the TDP simple is then an obvious goal, so certain processors will have the same TDP in their spec, even when they obviously vary in actual power and heat output. This goes for both AMD and Intel procs, if you browse through the specs of their respective product lines.
Naturally, overclocking will change the picture dramatically, which is why aftermarket coolers are necessary in the first place. Once you overclock, TDP can shoot up dramatically, so forget about the specs, and forget about the stock cooler (designed strictly up to the rated TDP of the proc, overclocks that may push TDP over the official spec not taken into account) being adequate.
EDIT: Didn't see if you were using an aftermarket cooler, but if I remember right, the X2 555 BE is 95W and uses the bare "block of aluminum" cooler, correct? If you are still using that cooler, that's hardly adequate for any X4. The max rated TDP for the aluminum cooler is 95W, as opposed to 140W for the nicer AMD stock cooler from AVC that has four heatpipes (as far as I know, it comes stock only for all 125W and 140W product lines)