If you send me a self addressed stamped padded envelope, I'll send you one of these.
It's a Tekmar 071 universal temperature sensor. It's a thermistor. It changes it's resistance very precisely with changes in it's temperature. You simply measure the resistance across it, and you enter that resistance in the chart on page 3 of this PDF file, and read off the temperature.
I replaced it hoping that one of the problems with my boiler was due to a faulty sensor, but it turns out the old sensor was OK. So, I replaced a good sensor with a new sensor, so I have a good sensor I don't need.
You can guestimate the temperature to + or - 1 degree F using the chart just by eyeballing based on the resistance, but you can also mathematically interpolate between resistance readings to get a much more accurate temperature reading (to well within one degree F). Thermistors, by nature, are very accurate, but the accuracy with which you measure the resistance will probably be a limitation here.
To overcome that limitation, you might just work in ohm rather than degrees, knowing that higher resistances mean cooler temperatures. After all, you don't need to know the temperature precisely, you just need to know if the water coming out one faucet is significantly hotter than the water coming out another.
Use a pair of wire nuts to connect the leads of the thermistor to the probles of your digital multimeter, hold the thermistor by the leads with the sensor bulb immersed in the water and wait for the resistance reading to stabilize. Then, convert that resistance reading to a temperature.
It's good from -60 deg. F to 255 deg. F and at room temperature (25 deg C), it's got an accuracy of 0.2 deg. C or about 1/3 of a degree F. The sensor bulb is metal and it appears to be well sealed, so I don't think immersion in water would harm it.
Private Message me to get my mailing address. Make sure to send a PADDED envelope since the hard metal sensor bulb is 3/8 inch in diameter and 3/4 inch long. I'd be concerned that putting that in a normal paper envelope would cause the envelope to tear in the mail sorting machines. A padded envelope would work a lot better.