No condiment will make a ___ sandwich taste good--enforcing boundaries is hard, firm work, and isn't easy on him either.
However being strong, firm, even hard isn't the same as being cold.
Not contacting him doesn't seem cold... . unless you are ignoring him reaching out to you.
He really needs to learn to self soothe. I am not letting him dump his anger on me or the kids anymore and he knows that from previous boundary setting.
You are correct about both statements. Please remember that there is a big difference between them:
HE picks his own schedule for learning to self-sooth; you have no input on that.
YOU choose not to let him dump anger on you or the kids. you can remove that choice from his menu.

Good work on doing it, BTW!
If you consistently do this, he has much more reason to learn better techniques of self-soothing... . but it is still his choice, not yours. Make sure you aren't doing things intended to "make him learn to self-sooth."