Suspended in a vacuum you have a red cube at 100 degrees and a blue cube of equal size and shape at 0 degrees.

You want to warm up the blue cube and cool down the red cube. The naive thing to do is touch them together, letting thermal redistribution eventually bring both to 50 degrees.

Lets say that you can slice the cubes up into pieces and touch small pieces together. Is it possible to get the blue cube hotter than 50 degrees? How hot can it get? (In the end you have to put each cube back together and wait for each cube to resolve to its average temperature.)

You may assume that objects touched together will resolve to a temperature that is the weighted average of their individual temperatures. You may also assume that there is no heat lost to the environment.