Explain to the class exactly what you are doing and what is happening. And, get yourself a digital multimeter, and have the bike on its rear stand with the rear wheel off the ground.
Take the seat off, set the multimeter to measure DC voltage, measure voltage across battery terminals. Key off, engine off. What's the reading?
When you turn the key on and start the engine, what does the temperature display show (A) before starting the engine (if it displays it), and (B) immediately after starting the engine? If the bike has been sitting for some time, does this temperature display make sense given the temperature that the bike has been sitting around in? Many temp gauges don't display anything if the temperature is below a certain amount ... that's OK ... does the amount of time of running engine that it takes before the temp gauge starts showing anything, make sense given the ambient temperature?
With the engine idling,having just started it, again measure the voltage across the battery terminals. What is it?
With the coolant temperature *just* having started to increase above minimum, switch the engine off. Let it sit for 10 seconds. Start the engine. Is all normal?
Now, with the bike safely on its rear stand (and still below the temperature at which you report problems), pull in the clutch, flip up the side stand, shift into gear, and gradually let out the clutch as you would normally do if you were riding. What happens? If anything abnormal happens, what happens, and at exactly what step in this process?
Now go back to neutral and with the side stand in the same condition that it was in when you report the problem (up? down?) and hold that multimeter against the battery terminals and report voltage. Continue to monitor that voltage until you are into the scenario where the problem occurs. Again repeat the starting-off-from-a-stop scenario and describe what happens and at exactly what step the engine stops.
Immediately after the engine stops:
- What is the voltage across the battery terminals?
- Is the taillight still on?
- Is the headlight still on?
- After the engine stopped, did the instruments display anything out of the ordinary - particularly the fault-warning lamp?
- Go back into neutral. Is the neutral light on?
- Press the start button. What happens? Is it a "nothing", is it a "click", is it a "crank but no fire", or does the engine crank and start normally?
- That is a fuel-injected engine. Is the fault warning indicator on at any time when it shouldn't be?
We need as much information as possible. The subtlest little thing can be the clue to what's wrong.