I was originally going to mention Solar Beam as an option for the 4th slot, since it wouldn't be out of the question to run Exploud on a Sun team. I mean, it always runs at least one Fire-type move, after all. However, after running some calcs it seems Solar Beam is only ever useful to...
-guarantee the OHKO on physically defensive Rotom-W w/o SR (Boomburst has 50% chance to OHKO)
-guarantee OHKO on 252HP/252Att Swampert (Boomburst can't OHKO even w/ SR)
-potentially OHKO physically defensive Politoed (25% w/o SR, guaranteed w/ SR)
-OHKO Gastrodon (which isn't outspeeding Exploud, anyway)
-OHKO Slowbro (which again isn't outpseeding anything)
-nab the 2HKO on Carbink (which is barely used)
-potentially nab the OHKO on Vaporeon (18.8% after SR).
-guarantee the OHKO on Manaphy after SR (Boomburst has an 87.5% chance)
Anything else either would require both SR and at least on layer of Spikes, or just isn't used enough to be worth mentioning in the first place.
Having used both exploud and a powerful sun team on ladder I decided to give your suggestion a test. Let me just say this - its a heck of a surprise how strong Exploud is in the sun with Solar Beam. Yes there are many situations where Boomburst outdamages or comes close, but the times I've OHKOed Rotoms, Swamperts, gastrodons and slowbros is amazing (mostly rotom-w). The main thing about bringing Exploud onto a Sun Team is that the only thing you are losing into adding Solar Beam is Overheat - which is pointless when you get a SUN-BOOSTED fire blast / flamethrower.
- Boomburst
- Fire Blast
- Focus Blast
- Solarbeam
That's what I ran with with my sun team, and its extremely powerful. Boomburst wrecks, specs sun-boosted fire blast wrecks (fire blast instead of flamethrower because guaranteed OHKO to aegislash and in the sun, calcs below), Focus Blast destroys Tyranitar and Heatran like normal, and solar beam destroys Rotom-w, slowbro, vaporeon, swampert, gastrodon, etc. With Rotom-W having one of the highest usages its great to have a guaranteed OHKO. Again, especially since it's only at the loss of using Overheat which is just "the next best move to use because nothing else is better".
Some calcs:
252+ SpA Choice Specs Exploud Fire Blast vs. 252 HP / 4 SpD Aegislash-Shield in Sun: 326-384 (100.6 - 118.5%) -- guaranteed OHKO with fire blast in sun
252+ SpA Choice Specs Exploud Flamethrower vs. 252 HP / 4 SpD Aegislash-Shield in Sun: 266-314 (82 - 96.9%) -- missed OHKO with flamethrower in sun
252+ SpA Choice Specs Exploud Solar Beam vs. 252 HP / 0+ SpD Rotom-W: 290-342 (95.3 - 112.5%) -- guaranteed OHKO after Stealth Rock (75%
without stealth rock, boomburst has
0% chance to OHKO defensive rotom-w without stealth rock).
I don't know if its worth mentioning, but its just the fact that 1. Boomburst hits so hard and to then bring 2. A grass coverage move that hits even harder along with 3. Sun-boosted Fire blast to cover those that resist your main stab and 4. losing only a "filler move" in Overheat when placing him on the sun team.
Note: Forgot to mention, with sun up literally the only thing Rotom can do to you is volt switch out or you will force the switch as sun reduced Hydro pump does nothing (slightly less than volt switch if I remember). Usually I try get OHKO or 2HKO with boomburst without the sun, and rotom-ws punish me with Hydro Pump which does around half and OHKOs if I've taken a hit, but in a sun team it does less than
25%. Rotom destroyer?