How to reduce noise from my refrigerator?
Most refrigerator alcoves are mini reverberation chambers, having hard sides.  You may be able to place acoustic foam behind the refrigerator to absorb the sounds.

If you're handy sewing, you could copy this design for a sound reduction blanket using polyester fiber fill used for coats.  As a trial, just loop a couple of layers of the batting off a couple eye hooks and leave space for air circulation.  You may have to use some twine to  belt it down flat.  If it works, enclose in a cotton sack stitched down like a quilt.

To be clear, I'm only suggesting a flat wall hanging, nothing to trap heat.