Ice melts int0 7/7, yes. Magma does seem to melt in adjacent directions, but only 1 tile. Ice, a wall, and then magma, will cause no melting as the magma is adjacent to the wall, not the ice. However, magma above ice should work, as evidenced by murky pools. When digging my surface forts, I tend to put a small area underground as a basement, for underground farms, booze storage, and early workshops before I can set up the outer walls. When doing so, I often build on Z-2 to avoid murky pools, and I get digging cancels because of the murky pool above the digging site. This seems to imply that magma would heat up things under it, because moist walls and warm walls seem to function identically.
You should be able to build a whole floor of floodgates or doors above the ice, open them all so the area is clear, and then drop magma. This will cause melting of the ice. Closing the floodgates will atom-smash the magma and cause instant freezing. Because of the way floogates work, you could simply have a magma reservoir above the machine, directly linked. Opening the floodgates will drop magma, and closing them will destroy it AND prevent more from flowing in, making for a simple setup. A more complicated setup could be used to drop exactly 2/7 magma onto the melting plate, to conserve liquids and plumbing/FPS concerns, but would not be entirely difficult to set up.