There are quite a few questions on this sort of theme here, and I've also read one or two other things, like non-ballistic re-entry. So this might be a duplicate, but I don't think so.
To clarify: I'm not talking about using aerodynamic characteristics of the returning craft, at least not until the atmospheric speed has really been brought down to very low, mach 3 or so maybe.
I'm simply wondering: suppose you do a burn which slows you down from LEO, causing your craft to travel through the mesopause (coldest part of the atmosphere), just slowing you down (and heating you up) a tiny bit... your craft would then carry on beyond the confines of the circular LEO orbit effectively in a more elliptical orbit. At apogee of that orbit you then do a new minor burn to ensure that as you fall to Earth again you are once again on a trajectory through the mesopause, which skims off a bit more kinetic energy, and gives you a bit more heat. This trajectory again sends you off away from Earth to a slightly slower apogee. Your effective orbits would become more and more elliptical. But you'd be losing kinetic energy on each dip.
The idea would of course be to try and cool the craft between each dip. Just off the top of my head you might want to make use of the shadow of the Earth as much as possible (difficult because you are spinning round it, but some timings might be better than others), but also perhaps of the Moon sometimes. Also you might conceivably have a shield, large enough to cover the narrowest profile of the craft, which could be manoeuvred into place between the craft and the Sun, so that it would stop any solar thermal radiation falling on the craft. I read the idea somewhere that cooling takes longer than heating, but on the other hand maybe that depends on the relative time spent between dipping and cooling?
Doing a minor burn at apogee would mean that a small thrust would go a long way because at that point you would be going slowest.
The aim being essentially to kill the "orbiting" and at the end find yourself in a craft which was simply falling, probably from a very great height. But mightn't it be possible to reduce significantly the super-high speeds and temperatures of re-entry from orbit by such an approach? Maybe something like the Space Shuttle could be feasible using this approach, as it was killed off by extreme heat (or an inability to design for it).
NB some of the the heat might be used, fairly obviously, for keeping the inner temperature comfortable.
NB2 you might also scoop up some atmosphere on each dip: oxygen could be used for oxidiser and nitrogen for propellant, perhaps, to contribute something when tweaking your trajectory with the burn at each apogee...