Jed, please be aware that many, many vets start cats on waaaaay too high a dose of methimazole, and that can cause very severe and serious side effects, generally 2-3 weeks after beginning the drug (though adverse side effects like vomiting and inappetance can occur sooner than that). High dosing is very old school medicine, but unfortunately far too many vets haven't caught up with current dosing recommendations. The safe way to administer methimazole adheres to the adage, "start low and go slow", meaning to start at a low dose and slowly increase dosage should the need arise.
So, may I ask at what dose your vet has started your cat? If it's more than 1.25 mg twice daily, you should be doing your own research to decide if you are comfortable with the higher dose. Many folks start their cats at just 1.25 mg once a day.
I wish I'd known about current dosing recommendations before I started my cat, Billy, on methimazole. My vet started him on 2.5 mg twice daily. Within 3 weeks, Billy was so hypOthyroid that his T4 didn't even register on the lab equipment. It took about 7 months to get him regulated on a correct dose. Regardless of your cat's starting dose, be sure to have his T4 tested again no more than 3 weeks after beginning the med so that his dose can be adjusted, if necessary.
I strongly recommend you join the Feline-hyperT mailing list. Those folks REALLY know this disease and all of the ins and outs of the various treatment options. If you join the list and spend some time reading the current and archived messages, you'll learn a ton. And of course you can post any questions you may have to the list, as well. Here's a link to the list:
I wish you and your cat all the best.