Oh duh! That makes sense. Though like I was saying I don't think you'd heat up. Think of the SpaceX boosters. They fall from at least half of ISS orbital distances, and don't even heat enough to create vapor.
The Shuttle reaches a maximum of about about 1,650 C with a re-entry of Mach M or Mach ~25 (7823.2mp/s) (And even at this speed it's a gradual inclination to the atmosphere, not a steep fall).
Also, I'm unsure those falling characteristics are still that accurate when you consider mass of on object which place a significant role in gravitational pull. For example, it takes more delta v to lift said mass into orbit, it also plays a roll in descent.
It'd be weird for a person to gain the speed you suggest (2400mps), as it suggests if it were able to continue falling, you would gain orbit (7666mps equatorial), or break orbit from Earth which just wouldn't make sense.
Ballistic Flight is not free-falling, it is defeating gravitation influence without aerodynamics. Flying is lift via aerodynamics, Spaceflight is lift via delta v, or acceleration only. Saying it's freefalling means all flight is freefalling which is just silly. Freefalling is freefalling, from a fixed position under gravitational influence without thrust. For example you could be using spaceflight for ascension, which would be the opposite of falling towards the gravitational influence until you break the SOI.