I definitely found this one easier to see with the grid topology effect, which is that each digit must appear in one of: a diagonal pair of corners, a corner and the middle of the three opposite faces, or the middles of all six faces. When you found that there are two repeats on the arrows, each repeat must therefore be both cells of an arrow or both circles (because those are your diagonal pairs of corners), and putting both repeats on the arrow cells doesn't work. Then the diagonal arrow with different digits has to avoid putting a triple of faces somewhere that gets both thermo cells. (The proof from my earlier comment: Each cell is in 1 or 3 regions, and there are 6 regions. The ways to make 6 out of 1s and 3s are: 3+3, 3+1+1+1, and 1+1+1+1+1+1.)
I definitely found this one easier to see with the grid topology effect, which is that each digit must appear in one of: a diagonal pair of corners, a corner and the middle of the three opposite faces, or the middles of all six faces. When you found that there are two repeats on the arrows, each repeat must therefore be both cells of an arrow or both circles (because those are your diagonal pairs of corners), and putting both repeats on the arrow cells doesn't work. Then the diagonal arrow with different digits has to avoid putting a triple of faces somewhere that gets both thermo cells.
(The proof from my earlier comment: Each cell is in 1 or 3 regions, and there are 6 regions. The ways to make 6 out of 1s and 3s are: 3+3, 3+1+1+1, and 1+1+1+1+1+1.)