I have yet to try this, but I think it may be possible. I believe there will be some required pieces of gear, namely the Void Star Talisman. I also believe that a Demonology spec will be required, with
Here's my planned strategy:
Pre-fight: Equip your Void Star Talisman, of course. Get any buffs you can. It might be a good idea to have some other fire resist gear on.
Phase 1: Nuke down Thaladred while kiting him. Let your Felguard solo the next three adds while you heal him. Try and stack them all in the same spot, with Capernian a bit away from the others.
Phase 2: When the weapons pop, go Meta and hit them with everything you've got in terms of AoE, making sure to have Felstorm available for this. They've only got ~100k each with the shield having about 200k. I'd focus on the mace with the Felguard's single target as well as the stun so it doesn't heal. Pick up the staff and put it on, making sure to use the aura.
Phase 3: When the adds all rez, nuke down Thaladred as quickly as possible, making sure to heal your Felguard. Once Thaladred is down, focus on Sanguinar, as the Fear doesn't get negated by the staff. Once he's down, move on to the other two.
Phase 4: When Kael'thas activates, send your Felguard onto him to try and draw aggro. His fire resistance from the Void Star Talisman and any other gear you might have should be pretty high, making for pretty easy healing. The tricky part is the Pyroblasts, but between the fire resistance and his high health, he might be able to live through this. An alternative strategy is to tank him yourself and spam Drain Life the whole time, then pop a Soulburn + Healthstone before the Pyroblasts and tank one, then Soulshatter and let your pet tank the other two. Assuming you can live through this, you should be good. Burning the Phoenix Eggs should be pretty easy.
Phase 5: Nuke his face? If you've gotten here, it should be pretty easy.
Looking for ideas on this. I don't think you can be MCed if you're the only person there, though it might MC you if your pet has aggro (Malchezaar will use Enfeeble, which is hilariously bugged to sometimes kill you instantly instead and rez you after the duration is up).