Hotter the better, coin expands (very very slightly) interupting the coating of years of gunk, and the detergent works better when in hot water solution.
That's what I find compared to cleaning in cold water.
Shot of hot water from the kettle in to the glass every time you make a brew keeps things going.
The longer you leave it to soak, the better the results.
Try it.
If you want to get really intense........
after the prolonged soaking clean coin with a toothbrush with some neat washing up liquid on it, rinsing off under a warm/hot tap, repeat toothbrushing /rinse / repeat etc.
I use my old electric toothbrush, soft bristle attachment, very light pressure.
Idea is to get the coin to spin in your hand as your cleaning it.
There you go , that's my secret technique