Does Heat vary within different Tiers?

Now, I know I'm going to sound clueless, but I've heard rumors here and there.
So my main question is;
Does the amount of Heat you earn vary within different Tier runs?
Or does that only apply to Crowns?

To add a little more detail: We don't know exactly how heat varies. It seems to go up, as you go deeper into the Clockworks. There is currently a thread attempting to quantify things, but don't hold your breath.

You can instantly heat a 1* weapon from level 1 to level 10 at a stratum 4 arena if you don't die.
(well, that's what I tried when Rise or Fall was a slime arena.)

It seems to me to be that even numbered stratums give more than odd numbered. Like, say, a D6 arena vs a D10 arena. Might just be my imagination, but S2 arenas give surprisingly decent heat.

I think I'll have to experiment with this. Thanks to everyone.
Yes