Hello, and welcome!
Yes, a symptom of hyperthyroidism can be vomiting, but also, if he was started on oral medication for hyperthyroidism (methimazole), this can also cause nausea in some cats.
I'm glad the vet gave you easily digestible food for him, and there is also a Science Diet prescription food especially for hyperthyroidism, called Y/D, so you can discuss that possibilitywith your vet, as well.
If Bart is nauseated, you can give him 1/4 of a 10 mg. Pepcid AC (Famotidine) tablet 20 minutes before his first meal of the day and this over the counter acid controller, should help. Here is more information: CLICK
Try to feed him smaller meals more frequently and see if that helps.
You don't want him to become dehydrated if he is only throwing up clear liquid, so add some children's unflavored, clear Pedialyte to his water bowl (50/50) to restore any electrolytes he may be losing.
I hope all will be well with Bart and please let me know how he's doing. Thanks!
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