I don't use hot water very often on my Omega, but I have done it. The only reason I see for using a liquid soap is to break the surface tension of water, which helps it penetrate much better.

You will get burns from the water before it's anywhere near hot enough to start melting the sights.

I do not remove my stock for everyday cleaning, I remove no more than once per month to do a deep cleaning on it. I never remove the trigger assembly. I see no reason for it, the trigger assembly is cleaned when I clean the barrel and breech.

The way I do clean my Omega:
Run a swab with bore solvent on it;
Run the brush through it,
Run another swab through to get the heavy crud,
Remove the breech and soak it in solvent,
Spray some type of foaming barrel cleaner into the barrel and trigger assembly, then I let it set for about an hour or so in the tub (my wife LOVES that part...)
Hose it down with hot water out of the shower to rinse the trigger assembly, I try to keep from getting anything else wet.
Dry the trigger assembly with a rag, it doesn't need to be totally dry, just pat it down to get most of the water off.
Brush out the bore one more time, then run swabs through till they are clean, it takes 2 or 3 swabs before they are clean.
Spray it all down with WD-40, swab the barrel and dry the trigger assembly.

If you soak it, make sure to remove the stock, you will have to anyway to dry the barrel under it. Water will also get under the scope mount and the sights.