I tend to avoid compression. I try to get transients right at the source, and I use bus compression very sparingly. I do however route all sorts of things through my Korgasmatron (dual analog filter with clipping circuit), and I like how if you get the settings right the big transient peaks get flattened but sort of replaced by a nice analog clipping sound.
So my question is how you feel your transients are treated by the Heat. Do you use Heat as a dirty limiter? Do any of the circuits have soft-knee characteristics?
I must say I have not enough knowledge to really answer you right know.
All I can say is that with the three levels (drive, FX level, wet level) + EQ and the numerous distorsions you can polish your sound very precisely.
Add now the multi mode filter, and I canāt see how you would not be able to tailor the sound exactly the way you want. And find a zillion interesting sweet spots in while looking for it.

Iāve fallen in love with how this little box can really transform the sound that get through it for the better, in amazing ways you wouldnāt imagine on the paper.
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You can definitely get straight up distortion / clipping / dirty limiting with AH. That will give the effect you describe: peaks are āreplacedā by clipping. Iām not sure about the exact characteristics of the eight different distortion circuits. I just use my ears. 
The filter also has ādriveā which can add another level of distortion.
However, the AH can go far beyond that: You can have the envelope follower modulate the wet/dry mix or the wet level to get a combination of compression / clipping that really doesnāt sound like anything else. For me, this is where the magic is. 
It goes on from there.
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With drive/wet/ratio controls on HEAT you can control dynamic very accurately: you can have almost no effect on dynamic and very transparent transient response to completely crushed soundā¦up to you. I canāt answer for sure, but for me āsoft distortionsā (those on the left side) have soft-knee like characteristics, and you can obtain very nice subtle ārounded/analogā percussive sounds out of it.