Agree that tube pre + SS amp is a good “warm” direction to go from the Hegel H390.
A GanFet amp, which is similar to a warm sounding SS, may be a good option.
Krell K-300i integrated has “150Wpc into 8 ohms and 300Wpc into 4 ohms, with its iBias technology allowing the amp to deliver up to the first 90W in class-A (warmth) —"without the excessive heat and power consumption of traditional Class-A designs,- (Stereophile)