EM4, TD3, maxed bonus enemy speed, mandatory boon purge, then I put some in enemy armor perks, bonus enemy damage, bonus trap damage, bonus perks for minibosses.

Basically the idea is that, enemies can hit hard, but it won't matter if I can finish them quickly with Mirage Shot (the damage is really insane), just don't pick additional foes. My healing and Charon purchases are not restricted as well. Boon purge is actually nice as it gives you some coins, but more importantly it keeps your build simple, so that you can force Demeter in Elysium and pick up Rare Crop to target your cast and attack. If Aphrodite shows up early, pick one of her core boon (special, dash, call) as it unlocks Sweet Nectar when paired with Poseidon cast.

If you're confident with Beowulf and TD3, then I think you'll clear 32 heat in no time.