Diesel cars will have a lot of issues from a cold engine way before the diesel freezes outright (diesel sold during the winter typically have freezing points below -40C).
For instance, the battery charges really poorly when it's cold, diesel crystals can form in the diesel filter, even if the fuel is technically liquid, and the engine is really inefficient if it's too cold.
Of these, the battery not charging properly, coupled with a lot more electricity needed to start the engine when cold, is probably the first one you will encounter. If it's -20C, you may have to charge the battery once every few days using an external charger, if you mostly do short to medium trips.
I live in Norway, were we can get quite cold weather too, and the typical remedy is some kind of engine heater, fueled either by electricity or by the car's own fuel (for newer models, mostly).
There are several types of heating elements, some heat the cooliant (heatiant during winter), some heat the engine oil, and some just heat the underside of the car. All can contribute really well to the problems you get down to -40C or a bit below, at least if they provide enough power (some may be underpowered if the car is exposed and it's really cold) I think these will melt crystals forming in the diesel filter, and once the engine is started, diesel will circulate through the engine, ensuring that the fuel in the tank reaches an acceptable temperature sooner. Also, a warmer engine requires a lot less electricity to start, meaning battery issues are less likely.
While I don't think most of these are designed to heat the fuel tank directly, they probably generate enough heat that some of the heating will spill to the fuel, too, especially if the car is sheltered in a garage.
And if the temperature outside falls well below -40C, you can probably heat the garage using a lot less energy than required to keep the engine running.
Keeping the engine running 24/7 in any location where electricity is available, doesn't seem like an efficient solution unless you're deep in Siberia and fuel is subsidized but electricity is not.