Okay, honestly, I thought that Sothmekhmet was just OP when I first encountered him. 16,000 health? Seriously? And a Storm minion that constantly Tritons you? I have the solution to all of your problems.
Okay, first, do whatever you can to take out that minion quickly. He's the line between life and death for you. Use helephants, phoenixes, dragons, whatever you can in order to get that minion out. When you take that minion out, be prepared to be bored out of your mind. The battle will take a long time, but it will all be worth it with your Efreet. First of all, do not use any charms or traps. He will cheat-Hex you, and this can kill you. So don't pack any of those in your spell deck. What you do want in your spell deck is a bunch of Thermal Shields (Sothmekhmet always uses Colossi and Icezillas) and Links (the health is very important). Use as many of both Links and Power Links as possible! These are extremely important. Another tip for this battle is to use a Wyldfire after you kill the minion. The reason for this is that the minion can use Darkwind. However, Sothmekhmet doesn't have any "bubble" spells. After you use up all of your links, Sothmekhmet should be almost dead. Use a strong attack, such as a Helephant or Phoenix, to kill him. A major tide-turner for the battle is to use damage enchantments. I brought many Monstrous and Gargantuan cards to the battle, and they helped me so much. You can get all of the Sun school spells after Strong (Giant, Monstrous, Gargantuan, but not Colossal) from the Sun School trainer in The Floating Land.
Have fun with your new Efreet spell, and I hope that this helps you!
Logan Darkflame, level 78 Pyromancer "Don't Mess with the Keeper of the Flame"
Sideboard cleanse ward and shatter were very useful
Extra bubbles and extra auras (mostly Infallible, but also Amplify) were helpful. Getting through tower and ice armor was nice.
Spam gargantuan elf and link like there's no tomorrow. Early game, hound is good; late game, you're probably hurting so you just want to hit the same turn you blank your pips.
You're never going to get a crit on this guy, so if you were looking at ice resist armor but preferred something that boost your crit, now's the time to look again. If it also has storm resist, then that's a plus.
Pets with may cast abilities don't trigger the cheat, so may cast fireblade and fuel and all that are nice.
For the record I loathe op cheating solo-only spell quest bosses. Either make it a fair solo-only fight, or let your buddies come and help you.