You are correct, they only come on to start the engine, usually only a few seconds, however with colder weather the plugs stay on longer. If the engine has stood over night then the surrounding environment would be an ambient of lets say 0 degrees, a diesel relies on there being enough heat within the compression stroke to ignite the fuel/air mix at just before tdc. If the surrounding cylinder walls are all at 0-1degrees then the charge requires a lot more heat to warm it up, thus the plugs stay on longer to help it out.
You can do a very rudimentary test by starting from cold, letting it run for a minute, switch it off, then start it again and see if the same happens. It shouldn't unless it is very VERY cold.