My mechanical meat thermometer is taking an average of the meat and air temperature I have two "good cook" brand mechanical instant read meat thermometers.  I use my small oven broiler to cook steak to medium rare.  However, after cooking for a while, taking the meat out and measuring it with both thermometers, the temperature never reaches above 120.  In the end, the meat is quite dry and obviously ruined.

I did a test with a boiling cup of water.  If I only dip the probe tip into the water, the thermometer doesn't read 100 C but rather something much lower (consistent reading on both thermometers).  If I immerse the entire probe in the boiling water, it would read close to 100C.

I suspect that these probes actually average the temperature over the entire length of the probe.  But this would mean that I cannot really rely on these thermometers to diagnose welldone-ness.  Had anyone else ran into this issue?

I suppose I could re-calibrate the temperature reading at which my steak is considered rare, most likely a reading of around 100 F on these thermos.
You are right that mechanical probes sense temperature along the length of the probe, so they are only accurate if they are almost completely embedded in the food. Electric probes on the other hand have a thermocouple at the tip of the probe, so they are much more accurate. I suggest you get a digital probe instead.