Offroad-Express

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Often white smoke is a sign of a cracked head.
Im guessing it has a crack in the water jacket allowing water to seep in & when you start it up from cold the water turns to steam hence the white smoke.

Is there any sign of oil in the radiator?
Is the radiator "bubbling" when the motor is running ?
Do you have to keep topping up the radiator ?

Any of these 3 could confirm a cracked head.

White smoke a sign of unburnt diesel also.
Check the glow plugs.

TD27 has a cast iron head so I doubt it is cracked. They're a fairly bullet proof motor. Good old cast iron push rod design.

Isn't there also the off-chance that there's water in the exhaust pipe which would evaporate, causing the same effect?

If it lasted longer than a few seconds then I'd be a bit more worried.

White smoke on cold start can be unburnt fuel, it can be caused by worn injectors and pump, if it had a cracked head which i doubt, it wouldnt just go away when warm.

Old Safari had a problem with the fuel pump, which caused white smoke, but only when cold.
80 series was the same until I got the injectors reconditioned a couple of weeks ago.

The cause of White smoke is Compressed but not ignited Diesel.
Usually the causes of this is Glow plugs/Valves not sealing properly/Low compression/Timing.

Yep as said above could be pump timing.
My 3b blows the same on cold start up but the fella who recoed the engine said to drop it down and he will set up the pump properly