All valid suggestions. Tweaks and isolation devices for equipment (and speakers) such as Nobsound springs or other equivalent products will be useful. Apart from these products, room furnishing or treatment and placement of speakers will also help.
Nevertheless, I understand you are asking for a warm sounding amp. I can only advise based on my experience. You want an amp that will not sacrifice clarity and detail at the expense of warmth. Some amps will mask the detail, or perhaps fail to reproduce the detail. Some of the detail may be rolled off in the treble. You may appreciate the reduced energy in the treble but that’s not accurate sound reproduction. What you want is a sound that is not bright or harsh but still has that illuminating glow or energy with good clarity and detail. Some amps may sound smooth but are capable of reproducing the clarity and detail, a hard act to follow. The inferior amps sound smooth and warm and at the same time lack the clarity and detail, sounding like mud.
All amps are colored to a certain degree and it would be useful to pick one that doesn’t sound too colored.
To cut to the chase, an integrated amp which sounds smooth and slightly warm but still has great clarity and detail is the Class A Luxman L-590AXII. This was mentioned before above by another member. To me it sounds very close to neutral.
As Millercarbon has aptly pointed out, don’t overlook the isolation devices or other tweaks as they can fine tune the system and produce great results. Get the basics right and you will be on the right track to achieving a great sounding system.
Good luck.
