Brain teaser helpp! ?

Turn on the first 2 switches. Leave them on for 5 minutes. Once 5 minutes has ped, turn off the second switch, leaving one switch on. Now go through the door. The light that is still on is connected to the first switch, whichever of the other two is warm to the touch is connected to the second switch. The bulb that is cold is connected to the switch that was never turned on... right?