1st Ability — Pyrotechnics:
“Blast targeted enemies with pillars of Heat Damage. Backbeat Timing: Ignite even more pillars. Increases the Duration and Heat Damage of Ripper's Wail when it deals damage.”
On Backbeat timing the metronome, Pyrotechnics gains 2x the pillars in total, adding 5 more pillars to the original cast. Performing a Backbeat cast also steadily increases the Ripper’s Wail damage bonus. Pyrotechnics is a weapon scaling ability, meaning Arcane Arachne, Nourish, Eclipse, and Vigorous Swap all benefit the ability. Pyrotechnics also procs a FORCED heat proc, which can scale the ability to stack damage exponentially as heat procs increase on the target.

MATH TIME:
1000 Base Damage
5 Pillars x (2 on Backbeat Cast)

Base Equation:
Damage/Pillar = 1000 x (1+Strength Mods) x (For Each Universal Weapon Bonuses)(1 + Weapon Bonuses)
Universal Weapon Bonuses like Arachne, Eclipse, and Nourish
Total Damage = Damage/Pillar x 5 x (2 for Backbeat Cast)

DoT Base Equation:
DoT Damage = 0.5 x 1000 x (1+Strength Mods) x (2 for Archon Vitality) x (For Each Universal Weapon Bonuses)(1 + Weapon Bonuses)
Ripper’s Wail does NOT increase the DoT, nor the damage (anymore) of Pyrotechnics. Big sad.
Nourish Bonus definitely does NOT scale the DoT.

The big issue with Pyrotechnics is that it will divide the pillars among the enemies on the field, so we will see a large damage drop off since the pillars are both randomized on the target enemies and it only applies 1 damage instance. I love this ability for other warframes that can increase the damage further like Mirage, but there are helminth abilities that take the cake in this slot.
Moddable by Duration, Range, and Strength

2nd Ability — Overdrive:
“Drive loudspeakers into epic distortion to create a damaging wave of Heat Damage while also increasing vulnerability to Critical Chance. Backbeat Timing: Doubles Critical Chance. Increases the Duration and Heat Damage of Ripper’s Wail when it deals damage.”
Overdrive’s wave works in a 100° FOV and reaches out at a base of 20m. When Backbeat casting Overdrive, the enemy becomes vulnerable to crit chance for DOUBLE the listed value. This crit chance is a final additive crit chance increase, similar to puncture procs or Arcane Avenger. Alongside the critical chance increase, enemies are temporarily stunned for 2 seconds as their eardrums are blasted full of Stardust glitter and Unicorn screams.Demolishers and enemies with Overguard do not receive the stun, womp womp. Not every ability is as good as Damage Decoy or Condemn. This ability also increases the Heat damage of Ripper’s Wail, further supporting the decision to swap out Pyrotechnics for another ability.

HERE’S THE MATH:
750 Base Damage
25% Crit Chance
20s Duration

Base Equation:
Crit Vulnerability = 25% x (1 + Strength Mods)
Backbeat Timing = Crit Vulnerability x 2

Our Crit Vulnerability:
Crit Vulnerability = 25% x (269%)
Crit Vulnerability = 67%
Backbeat Timing = 67% x 2
Backbeat Timing = 134%
Moddable by Duration, Range, and Strength

3rd Ability — Ripper’s Wail:
“Rip on the guitar to make Temple briefly invulnerable while healing them. Ally’s weapons in Affinity Range are lit-up with extra Heat Damage each time an ability is used on the Backbeat and successfully hits enemies. Backbeat Timing: Invulnerability lasts longer.”
This ability is fucking awesome! Ripper’s wail adds an additive elemental damage bonus to your weapons: Primary, Secondary, and Melee, in affinity range for all allies within it, up to 750% heat damage. Holy hell, pun intended. This ability can have its timer replenished for every Backbeat cast of Pyrotechnics or Overdrive, causing it to essentially last forever. If your shields break and your heart starts racing, hit the 3. Although the ability states “invulnerability,” I noticed that without Primed Sure Footed, Temple would still manage to be knocked down with the grey bar. This could be latency, but who knows. Backbeat casting Ripper’s Wail will grant 4s of additional invulnerability after the ability animation ends, allowing us to go ham on the guitar and play that sweet heat. Not only that, the actual animation will fully heal us and grant the maximum amount of overshields for the full 2.5s shield gate by the time the animation concludes. Remember that 750% extra heat damage? Well.. it gets better. The damage bonus on Ripper's Wail increases the DoT of heat, additive to Elementalist. This means we can scale Heat mods and stack Ripper's wail to have a multiplicative effect between the mods and Rippers. The DoT goes fucking crazy!
Moddable by Duration and Strength

4th Ability — Exalted Solo:
“Once a charge has been built up on the Backbeat metronome, set Lizzie aflame and torch enemies with Heat. While aimed, Lizzie blasts enemies with thunderous elemental sound waves, use ability controls to change the Elemental Damage type. Backbeat Timing: No Energy consumed.”
Lizzie is Temple’s other half. Similar to Wukong and the Twin or Sevagoth and the Shadow, we now have Temple and Lizzie. The Duality in nature of the Luckstruck GlamRock Bandit and their Sensational Lovestruck Guitar. Offbeat timing forces 1 guaranteed status, and the Backbeat timing forces 3 guaranteed elemental procs for any of the Sonic Sigils: Viral, Magnetic, Cold, and Corrosive. On PC the best platform, you can both shoot the flames from Lizzie and cast the Sonic Sigils at the same time. From my experience with other testers, the controller makes it hard or impossible to do both. I’m sorry if you’re in that position.

We’ve gone down the rabbit hole of where to invest [Temple]’s shards, and similar to Cyte-09 and Ivara, the Electric Primary Damage shards called to us… Like the One Ring. We got Blast, Electricity, and Heat, all bundled together like a fruit rollup filled with gushers. Electricity felt like the optimal choice to weigh in because it tacks onto the Raw Damage and DoT, while the 750% Heat scaling from Ripper’s Wail will NOW scale the Heat DoT (ELEMENTALIST SCALING), and the 600% Electricity damage from the Archon Shards add another element to Temple's kit. Blast is modded in to stop Electricity and the innate Heat from becoming Radiation. Now we have a triple DoT weapon with massive raw damage along with most of the weapon DoTs scaling well into level cap.

Lizzie Build
https://overframe.gg/build/846155/lizzie/lizzie-gas-build/

Also for archon shards u would go with:
crimson shards on ability strength/duration