Yes, but if prices are high enough that demand destruction (a euphemism for "the poor can do without") is occuring in both gasoline and heating oil (a distinct possibility this year), then not enough heating oil will be produced to allow everybody to adequately heat their homes; thus, the rich will continue to drive SUVs while the poor freeze to death.

In another part of this thread, somebody pointed out that Congress could dictate to refineries that they have to produce enough heating oil to supply all residential heating requirements for the winter, even if it cuts into their bottom line (because the rich are willing to pay more for gasoline than the poor are able to pay for heating oil). My question is whether or not Congress will be able to muster the political will to do so (after fending off accusations of being communists) in time to really make a difference this winter.

This all may be moot because we are not currently short, and with any luck (and perhaps a mild winter) we can avoid a heating crisis this year.

If heating oil prices stay anywhere near the level cited by Fatbear, refineries will shift as much of their production as possible to take advantage of the it. Heatng oil prices higher than gasoline mean great margins for refiners. However, their equipment will be the main constraint on how far they can go.  With a given set of refining equipment, there is a fixed range of gasoline/distillate production levels.  The government can't order refineries to produce more than they can. However, you are right that the poor may not be able to bear the increased costs created by a product shortfall.