| You are right not to short across the sensor, that won't do any good at all. The fan can be tested by connecting the ECU to a Mathesis tester or the Technoreseach VDSTS but in the absense of these it is difficult to establish why it's not coming on.
You could start by disconnecting the fan and applying 12V across the pins of its connector. If the fan doesn't run then it's fecked. If it does then you'll have to look elsewhere. I'm not sure about the ST2 but on the 4s there is a relay under the seat which switches on the fan on getting a signal from the ECU. This would be a good place to start, as well as checking all the connections at both the fan and the relay.
If that turns up nothing then there are the 2 temperature sensors, they are both the same. One of them supplies the temperature readout in the instrument panel, the other is to the ECU. The ECU uses this to get information on the engine temperature and adjusts the fuel mix accordingly. It also uses it to decide when to switch on the fan. If the bike is otherwise running OK it is unlikely that the temperature sensor is faulty but you could swap them around and see if there is any difference but my money is on the relay.
Incidentally the fan on my ST4s doesn't come on until the display has reached 104C and that's only happened 2 or 3 times.  |