Have you also had Cortisol and sex hormones (Testosterone!, Estradiol & Progesterone)?
It is possible that you may be low on Progesterone and possibly tesosterone. Yes testosterone is extremely important to be present in the PROPER amount.
Low testosterone is commone symptoms is sleep disruptions as well as decreased libido. It is also extremely underdiagonsed in women because they do not even test for it often times.
My wife is low Testosterone. It took almost 4 full YEARS to convince my wife and our doctor that this was a major contributor to her symptoms.
My wife also has high heart rate. That cannot be explained by anything else. Other people report heart rate and breathing difficulties and abnormalities with low Testosterone.
Low T would not really explain too much the whole temperature intolerance. But as Barb135 stated above, hashi's (testing for antibodies) might. As swinging between Hyper to Hypo is not unheard of with the initial phases of Hashimoto's. As your slightly low Thyroid levels would also sort of lean towards only the potential of the early stages of Hashi.
Also check out your iron and Ferritin levels. Ferritin is needed for the proper metabolism of Thyroid hormone.
You may also wish to consider taking Selenium. It helps with the conversion from T4 to T3. However it is your FT4 that may be limiting your FT3. and since your FT3 is higher in the range than your FT4 level, it also suggests that you're converting pretty well. There may simply not be enough FT4 avaialable to convert fast enough for its use.
Ask your doctor to order the thyroid antibodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). These are the antibodies that are needed to diagnose Hashimoto's Thyroiditis. Hashimoto's is an autoimmune condition in which the body sees the thyroid as foreign and produces antibodies to destroy it. If one has Hashimoto's, it's possible for symptoms to appear long before the thyroid hormone levels actually go out of range.
In addition, with Hashimoto's, it's possible to swing between hyper and hypo for long periods of time before finally settling into a permanent hypo state.
Along with all that, some symptoms can "cross over" or apply to either/both hyper or hypo, though many people don't realize that. For instance, I had difficulty sleeping and shortness of breath when I was very hypo, so those aren't just hyper symptoms. Fatigue is another one that applies to both hyper and hypo... almost anyone that has a thyroid condition will list fatigue as a symptom.
On the flip side, decreased libido and memory loss can also apply to either hyper or hypo...
All of that said, your Free T4 is less than 50% of range and your Free T3 is at 57% of range, so neither of them are at max level. Most of us feel best when Free T4 is maintained at midrange and yours is at 43%, which indicates that your thyroid output may be less than optimal. We also tend to feel best when Free T3 is maintained in the upper half to upper third of range; yours is at 57% of range, which is okay, but with Free T4 less than optimal, it may be a matter of time before your Free T3 will no longer be adequate either.
You might also ask to get tested for Vitamins B-12 and D, along with Ferritin, which is the iron storage hormone. Many of us with thyroid conditions are deficient in the nutrients which are necessary for proper metabolism/conversion of thyroid hormones.