The temp sensor in the block, is this what you are referring to as a sending unit?
If so here is the way it works, first off the fan is normally wired with a relay, the relay uses battery voltage via the relay contacts to turn on the fan.
On the relay you have a coil with 2 pins, one is supplied by the same battery voltage .. The other pin will have a wire too the temp sensor, as the sensor comes up to temperature it goes to ground; the coil is energized;closes the contacts of the relay and the fan is turned on.
A quick check of the circuit can be done by simply removing the wire from the temp sensor and grounding it to the block, the fan will turn on. This tells you that the circuit is working. If the relay,or the fan or fuse if used, were to be bad the fan would stay off .
If the fan comes on grounding the wire and your fan does not come on when the car is at temperature, then the temp sensor has failed and needs replacement.
delawarebill is correct about the two pin type, so figure out the type you have, that will change the troubleshooting procedures.