With the ranges you gave me, the units of measure appear to be pmol/L.
I converted it to the units of measure and ranges I understand better --
FT4 15 pmol/L (12-22)
=> 1.17 ng/dL (0.93-1.71)
FT3 4.0 pmol/L (3.1-6.8)
=> 2.6 pg/mL (2.0-4.4)
Your FT4 is 31% of the range (goal no more than 60% of the range), while FT3 is 25% of the range (goal in the upper 25% of the range). This may show some slight inability to convert T4 to T3, but mostly it shows you could really use supplemental thyroid hormone. It makes sense that you feel so cold.
Your ability to convert can be influenced by good levels of serum potassium and serum sodium, serum Vitamin D at least 150 nmol/L (60 ng/mL), serum Vitamin B12 over the top of the range, adrenals well supported, and iron saturation 35% for women and 40-45% for men.
As you work on optimizing your ability to convert, do you also have access to thyroid hormone that preferably includes T3, not just T4?
I can't guess whether you can fix your thyroid problems with Iodine alone plus working on the conversion issues. Some on this forum have warmed themselves up nicely. Others, such as myself, have needed access to fully formed thyroid hormone.