To maximise DPS you will need the following components:
1. Roar : boosts ability damage by 1.82x, double dipping heat procs for 3.3124x
2. Armor Strip
Option a. [Hydroid] Specter: applies armor strip passively and allows Sol Gate to contribute to armor strip, as while haste mote is active, Sol Gate can proc corrosive status. As long as an enemy has been damaged by [Hydroid], reaching 10 corrosive status allows you to full strip.
Option b. 2 green +corrosive stack shards, allows full strip at 14 corrosive procs.
Option c. [Helios] with [Deconstructor] + [Vicious Bond] (means you can't use mecha set)
Option d. Helminth ability such as Pillage, Terrify or Tharros Strike (means you can't use Roar).
3. Heat Inherit: Using a viral + heat inherit primer first allows Sol Gate's heat procs to inherit the +heat mods (eg up to 225% from non-riven secondaries) for 3.25x more damage as well as one primed bane mod for 1.55x more damage. 10 Viral status also gives 4.25x multiplier.
4. Mecha set: [Mecha Empowered] allows you to increase heat proc damage on a [Marked Target] by 6.25x (double dips) and once killed, spreads the heat proc among all enemies within a 30m radius. Run [Huras Kubrow] so you can stay invisible.
5. All motes active: Health and shock motes provide a 25% damage increase each for a 1.5x final multiplier
6. [Archon Vitality]: doubles heat procs

With a maximum damage boosted beam hitting a mecha [Marked Target], adding all of these together the final potential heat proc damage per second when all the stars align, we get:

3000 (base dmg) x 2.74 (strength) x 2 (2 hits per second) x 0.5 (heat status) x 11 (after max boost at 5 seconds) x 1.5 (mote boost) x 3.3124 (roar) x 4.25 (viral) x 3.25 (heat inherit) x 1.55 (bane inherit) x 6.25 ([Mecha Empowered]) = 60 million heat damage per second.

Note that armor strip is mandatory to make this damage meaningful in steel path.