That might be true generally (and cities like New York and DC have really high per capita spending for that reason), but Baltimore is quite a bit less expensive than the surrounding suburbs. You can buy a gorgeously renovated townhouse in a nice neighborhood for $400-500k, a fraction of what it would cost in Montgomery County.
How expensive would it be to put space heaters in every classroom? Even window heaters are only $500. Surely a school district that spends $17m a year on maintenance can come up with that. My guess is bureaucracy/mismanagement is the real problem. The larger a school district is, the more bureaucracy.