The first form would be normal. It means I will go jogging tomorrow, and at the time I go jogging there will be no cars. I suppose this means that you will go jogging either very early or very late.
The second is odd I doubt you'd actually hear this being used - so what it means is a bit pointless. But I suppose it could mean that the statement about "no cars" is a description of tomorrow. And you expect that during all of tomorrow the streets will be empty.
It would be a pretty subtle difference and I doubt I'd actually understand that without thinking "hmm that is a pretty weird thing to say, I wonder if he means that their won't be any cars tomorrow."
It's pretty hard to find consistent interpretations of weird, counterintuitive, anti-pragmatic sentences. After all, in the real world, there are always some cars, even at 4 am, even on Christmas day. And since you understand in context, it is hard to unpick the subtle nuance of meaning when the pragmatic interpretation is acting against it.
If you did want to give the second meaning you would do much better to be explicit:
Tomorrow is the Emperor's birthday, and every has the day off work. Even driving is forbidden! I'll go jogging tomorrow because there will be no cars on the streets.