Blimey, that sounds like excitement you could do without. Stressful.
OK, from the smell of burning rubber, I'm thinking tyre. Have you checked the tyre?
The other rubber I think it might be is the caliper sliding pin boot. If your caliper siezed/severly dragging, which would account for the heat, it might have got hot enough to melt the boot to the point of smoking.
Have a look at eBay item number: 331774334522
I would suggest that is the situation. I would check to see if this is the case. If it is, buy the item above and fit the new parts. Clean everything when re fitting the caliper and make sure it is moving freely.
Hope that helps/make sense.
If not, ask away.
If you take the wheel off and are not sure, post a photo or two so we can 'see'.
This forum thread has a video that could answer a lot of questions
https://clubjazz.org/forum/index.php?topic=12830.0