Well all I got is the same story you did, but maybe we're interpreting differently.

I'm reading it as the landlord has no knowledge of the space heater, perhaps it isn't adequate for this particular unit, and the landlord hasn't attempted to provide such an alternative (given the timing of everything, who knows if providing an adequate alternative is achievable).

It's hard to say exactly how the law would apply here considering the VDHA document indicates a heating emergency such as this requires immediate repairs by the landlord but is fuzzy on the acceptable window of time and the law is also not clear on if the landlord is required to provide an alternative.

Of course, while not ideal, it may be prudent to temporarily put the OP into a hotel until the repairs can be made.