Over / Under active thyroid is certainly a possibility since with T1 you obviously already have at least one Autoimmune condition.
So you could be looking at Graves or Hashimotos, at the end of the day it doesn't matter which since both are treatable. As Gaz said for Hyperthyroidism (Over active) in the longer term they tend to go with radio iodine which knocks your thyroid out. You then have to be treated with thyroxine for the rest of your life, though that's just a tablet so nothing like T1.
If you are underactive then that would suggest they weight gain so I would say that's the most likely thing here. Treatment there is thyroxine tablets, so same as above just without radio iodine to first kill off your thyroid.
One thing to bear in mind is that it can take a while for them to dial in on dosages since they tend to work of TSH (Thyroid Stimulating Hormone) levels which can take weeks to react to changes. When they were getting my doses right after RAI I was going back every 9-12 weeks for a thyroid function test and then change of dosage.
As has been mentioned when your dosage is not right it can cause some unexpected variability in your insulin requirements, both basal and I:C ratio.
The only thing I can suggest is that you look at this as an obvious change and start with basal testing and then double check all your ratios as there will likely be differences. When they adjust your thyroxine (if under) or Carbimazole dose (if over active) you should expect changes so will likely need to watch for it.
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