Where can I find a transistor similar to a 2n 3904?
It's an NPN transistor- a very common one. You can find the data sheet easily by searching. They're around a dime each in small quantities from any distributor. 

They've tied the base and collector together so it's a diode-connected transistor.

Such a diode-connected transistor follows the ideal diode equation more closely than a real diode at lower currents. 

In the simplest implementation you put a current (say 100uA~1mA) through the transistor and it has a forward voltage of around 600mV that changes at about -2mV/°C. However the forward voltage and the tempco vary from unit to unit. 

By using two or three different currents you can cancel out the unit variations and also the resistance of wires going to the sensor by using a bit of math and choosing the currents carefully. It's possible to get interchangeability of sensors in the +/-1°C range typically without calibration or selection. 

This exact method is used to monitor CPU die temperature in a PC- the diode is part of the CPU chip. 

If you want to test if it is functional, many multimeters have a diode test function that should show a number such as something between 500 and 600 in one direction, and overrange (open) in the other direction. If it reads something like that, it's almost surely functional.