OK, lets look slightly deeper in the subject of avgas...and high(er) altitudes.
My previous statement that it doesn't matter about enroute temperature is correct, for most 4-engine piston airliners, simply because they most often did not operate above FL210.
Except for the B377 (Stratocruiser, and yes, I've personally flown this airplane, a joy to fly) as it went to FL230, on occasion.
Not all that high.
However...
The Consolidated-Vultee B-36 USAF bomber often cruised at /above FL400, simply because it had, in addition to an engine-driven supercharger, two General Electric quite large turbosuperchargers, which allowed high altitude operation.
The fuel?
115/145 octane avgas, delivered (oftentimes, refrigerated), to pack in more BTU's.
How do I know?
My neighbor down the street, that's who, and he was (now retired) a wing commander of 'ole B36's, long ago.
A bird Colonel.
I suspect he knows his 'stuff'.