how do I know if my washing machine is reaching the right temperature?

It starts to wash your clothes. Seriously - its automatic, and when it reaches the setting you have picked, it does begin the cycle.

Because you set the control to the wash cycle temperature you want. ie 30 degree cotton, 40 degree cotton etc.....

The machine uses it own internal thermostat on the heating element to ensure the correct temp is reached.

EDIT : Thats a toughie to tell, the only way is to A) feel the glass door and see if it's warm, or B) again feel the waste pipe going back to the sink waste and again check for temperature. Obviously, this is only a rough guide.

If you feel your clothes are not coming out clean then you may have to get a repair guy out but they charge a lot.

If your laundry is coming out clean and how you would expect it to then the thermostat is probably working fine. If the the water was not heating at all then it may continue to wash waiting for the water to heat.

Review your oracle sceptor.