I know that knob and tube wiring needs an air gap to dissipate heat.
I know that modern sheathed cable does not need an air gap.
I know both are made of copper, one is grounded, one not. So why does one need an air gap and one does not?
The air gap isn't primarily about heat. It's about electrical insulation. The fabric mesh that was used as insulation was not reliable, and could allow arcing and short circuits (especially if moisture comes into play). It's sort of the same principle you see in overhead power lines.
One could argue that there is a safety factor in the air gap with respect to heat, but the simple fact is that an electrical overload will heat the wires much faster than air could cool them anyway. This could allow the wires to burn or melt, or ignite combustible materials which they contact.
If this is about blown insulation, several western states repealed their codes prohibiting blown insulation over knob and tube.
Better science showed the large pool of such houses were not bursting into flames as the prognosticators had claimed.
The "air gap" theory is a myth. The size of wire used for K&T is the same as for modern wire, plus the joints are better.
The real issues are that most knob and tube circuits are undersized for the modern need, so many homeowners (and some electricians) upsized the fuses. Rest assured if you have 12 gauge wire and a 20 amp fuse, you're fine. If you have 14 gauge wire and a 15 amp fuse you're fine.
From Home Energy Magazine 'Knob and Tube Not a Fire Hazard':
Legislation was enacted in Washington state to allow insulating over knob-and-tube wiring per Bonneville Power Administration (BPA) specifications. This resulted because there were no documented cases of a fire being caused by knob-and-tube wiring, whether insulation covered it or not.
See also https://diy.stackexchange.com/a/20279/5960
K&T has huge advantages when it comes to driven staples and nails, and fire. It has theoretical downsides if blown in insulation gets wet. K&T wire insulation varies in quality from great to really bad -- but fortunately the K&T system does not require wire insulation.