Hi Foni1, welcome to the forum. Hurdity is right that being hypothyroid can rather complicate matters when it comes to menopause! However, there are several ladies on the forum who have long experience of thyroid disorders, so you will not be alone if you need support at any time.
Sorting out what symptoms are caused by which condition can be tricky. However, regular TFTs should help to ensure your thyroid meds dosage can be altered quickly if this becomes necessary as your gynae hormone levels decline. I'm long term hypothyroid & now a few years post-menopause & have had to alter my thyroid meds several times during the transition.
I'm not sure about the cold patches on your legs, though I certainly found that my hands, feet & lower legs used to get unnaturally cold during times I later came to associate with high levels of oestrogen - when periods were far apart & lack of ovulation allows this hormone to build. Together with the coldness in these body parts, I also used to feel tense for no reason - could be standing washing up with no particular stress then realise how cold feet & legs were & that my body felt as if I were about to sit an exam. Similar to the way the body reduces blood supply to the extremities when adrenalin kicks in. As chaotic production of adrenalin seems to be part of the response to fluctuating gynae hormone levels, this might explain it. Is your coldness in random patches though? Could also be that you need more Thyroxine of course!
Tests of gynae hormones levels can be very unreliable before menopause proper (ie before periods stop altogether), so many GPs understandably prefer not to do this unless there is a strong suspicion that something else is wrong. This situation can be a bit frustrating with a thyroid condition, as there's nothing to confirm you are definitely in perimenopause, other than suggestive gynae symptoms.
Flushes & sweats, together with the jitters, may make you feel as though you are on too much thyroid medication & as you'll know, it's important to make sure you are not over-treated for any length of time, so do flag this up with your doctor if it happens. This is the time to cultivate a good working relationship with a sympathetic GP who will listen & be willing to test your thyroid function whenever there's any doubt about the dosage you need. Good luck with the appt & do let us know how you get on.