Can I use a BC547 NPN transistor as a thermometer?
A diode (or a transistor connected as a diode as you have) does not behave like a resistor. Rather it has a voltage drop that doesn't change much with current, and has a slight negative temperature coefficient. 

If you use the recommended 47K resistor (passing about 180uA through the diode), then the voltage drop should be around 600mV and change about -2mV/°C. 

If you hold it in your hand you might heat it by 5°C and it would change by perhaps -10mV from (say) 612mV to 602mV (a small change percentage-wise). If you're getting ~600mV at room temperature, it's almost surely working correctly. 

The leakage current (what you are measuring on a high-resistance range) also changes with temperature, but it is not considered a reliable way to measure temperature. 

A transistor connected as a diode is actually more "ideal" diode than a real diode- the ideality coefficient is close to 1 vs. more like 2 for a typical rectifier diode or switching diode. 

The BC547 and 2N4401 work quite well in this application because they have low base resistance (better than, say, an RF transistor would work). 

The relatively large signal (-2mV/°C) can be traded off by comparing the voltage across a transistor at two different currents (or two tightly matched transistors operating at different currents) and this is how many monolithic temperature sensors work. You get only about 1/10 the signal (200uV/°C) but that's still plenty, and the unit-to-unit variation is very low. This method is used to measure CPU die temperature in computers.