The later model diesels had a very fast acting glow plug system, so it would not surprise me if, in the summertime, the glow plug light didn't come on when turning on the ignition. But coming on after 45 seconds is not right.

I doubt that the glow plugs(there is one for each cylinder) are the culprit here. If the light is coming on under these conditions, the problem is probably relay or wiring related.

Good luck,