Probably a lot. And that price will be tacked-on to oil prices (at least from that region), which will make it's way to the pump. Short of taking out Iran entirely (not really feasible) it will be permanent. Why wouldn't it be? Iran has everything to gain by making it permanent.

It would be permanent - it just won't be big enough to affect U.S. car purchasing decisions.

Information varies, but the speculation is that Iran is charging about $1-2 per barrel for vessels crossing the strait. Even assuming that 100% of that was passed on to buyers (which won't be true), that would only raise global oil prices by as much as $0.40 per barrel. Because "only" 20% of global oil production goes through the strait. That would correspond to about a one-cent per gallon increase in the cost of the oil input to gas. For Iran to raise U.S. gas prices by even a dime per gallon, they'd have to charge a $20 per barrel fee, rather than that $1-2 per barrel.

Could Iran start charging more than that $1-2 per barrel? Probably not for any length of time. $2 per barrel is about $15 billion per year, and the cost of a brand-new large scale pipeline crossing the whole of Saudi Arabia is about $8-10 billion. A $20 per barrel fee (again, raising U.S. gas prices by only a dime) would drive oil volumes through the strait to near zero within a few years. Which is the exact opposite of what Iran wants.