In that case I would put a voltmeter on the glow plug and see if it is still getting power. All the glowplugs I've seen do not get power that long. It's a big load on the battery, and might burn up the glow plug.
Also, the glow plug circuits that I am familiar with all control the glow plug based on how long it has been on, NOT on how hot it gets.
In most circuits, your ignition switch is just a trigger for the glow plug relay. The relay sends the high amps to the glow plug for a certain number of seconds and then turns off. The take-away is when you troubleshoot glowplug circuits where the light stays on or the glowplug doesn't seem to be heating, the problem can be in the glow plug relay OR in the glow plug itself OR in the heavy wire between the two.
rScotty