Somewhere Out There

I’m not singing, but somewhere, out there, beneath the pale moonlight, there are arrows and thermometers to fill the grid. Try to place all of the digits without flipping your lid.

Somewhere, out there, there’s no 6 nor 7. Out where dreams come true.

Rules:
Normal Sudoku rules apply.
Digits along arrows sum to the value in the attached circle.
Digits on thermometers strictly increase from bulb to tip.

Estimated difficulty: 2 out of 5