Hi Jules53,
any thyroid dysfunction can make symptoms at menopause very difficult to interpret, so you have my sympathies. As you will know, both palpitations & night sweats can result from an overactive (or over-treated) thyroid, as well as being symptoms of menopause. I've had thyroid problems (underactive) for more than 2 decades & have found the combination tricky to manage to say the least! I started HRT 3-years post-menopause & during changes of regime to try & find the best fit, have had recurrences of palpitations (ectopics) that had also been persistent in perimenopause without HRT. These & the intense, long-lasting night sweats & associated insomnia have been the most difficult symptoms for me. The uncertainty of which condition is causing what can really add to the worry, so I do feel for you.
The cause of night sweats is particularly difficult to be sure of for menopausal thyroid patients, so I would advise you to work closely with your GP/Endocrinologist to ensure that your thyroid condition is adequately monitored & controlled, with regular testing, especially in the first months adjusting to a new HRT regime. Even with transdermal regimes, which are thought to cause fewer interactions with thyroid replacement, I've had to make several changes to my thyroid meds dosages while on HRT.
Though as mentioned, my problem is underactivity rather than overactivity like yours, there were times when I was effectively hyperthyroid due to inadvertent over-treatment while gynae hormones were fluctuating & clouding the clinical picture. Though I am no expert on hyperthyroidism I imagine while you are finding the right HRT regime, your thyroid status could also be affected by the exogenous gynae hormones, making the night sweats etc difficult to interpret.
My night sweats have only ever been partially resolved by HRT (which I absorb poorly) & in my experience, any change of regime - increasing or decreasing HRT dosages, can cause these to worsen while the body adapts. It can be a question of perseverance finding the right HRT regime, but don't give up hope as symptoms should settle eventually & allow you to feel much better.
Can't stress enough though, that it's also important to be as sure as you can at this time, that your thyroid is under control. Now is the time to develop a really good working relationship with your GP & Endocrinologist! Good luck with it, keep posting & let us know how you are doing.