One of the most hypo t women I know of (on synthyroid)has a close to normal temperature. I find the meds confusing, as they seem to cover up the body`s real responses.
I prefer to go by the actual symptoms; a little low temperature is still no good, cold intolerance is hypo T (and possibly adrenal fatigue)
Yes I would increase the iodine, balanced with selenium and the others, and gradually reduce the meds, or change to a glandular ala Armour if possible.
When you are not hypo T, you will know, dont worry! - both the temperature, tolerance of cold and heat better, etc etc, and you have energy!