The rumor may be out of date, though I heard she was being considered for Veterans Affairs Secretary. The presumption Palin would go to Energy has been going on for some time (same with the one that presumed Giuliani would be AG), but Trump is shuffling the deck with unconventional considerations. Personally, I’d like to see Palin at State. The media heads would explode.
I wish people would keep in mind that the Department of Energy does very very little for energy. It is really the civilian agency responsible for defense nuclear weapons activities.
DOE's total budget for FY 2016 was $29.6M.
Of this:
$19.6 was for Atomic Energy Defense Activities: (Nuclear weapons, Naval Reactors (Admiral Rickover's outfit), and Nuclear waste clean-up (crony capitalism to pretend to do something about the legacy waste problem).
$5.7B was for Basic Science (national labs operating accelerators, etc.)
These activities were the province of the old Atomic Energy Commission which became ERDA under Nixon.
This leaves exactly $2.9B for energy activities and other assorted administrative tasks. Of this amount:
$638M is for fossil energy - this is a drop in the bucket, $2 / year per American citizen.
$1B is for nuclear energy (when was the last time that the DOE built a nuclear reactor?)
There is an additional $292 M for ARPA-E [DOE's venture capital effort after all the real venture capital firms have scraped off the good projects).