Total T3 is analogous to a fuel gage on your car. Sure you need gas in the car. But if none of the gas can get to the engine, then the amount of fuel in the tank is really moot almost useless information.
Free T3 measures the amount of gas getting to the engine. Which is what you really want to know.
You raised the specific question of TT3 being LOW, but both FT4 and FT3 being "adequate".
If you've read much here you know that the reference ranges are not optimized ranges. They are simply a statistic of the general population. So being "in range" means almost nothing. As a good portion of the population is low thyroid but do not know it. But since they are in the pool of data they tend to bring the whole "normal" range down. So much so that the bottom half of the FT4 range is questionable. Which is why you see so much on this site about if symptomatic and below 50% of the range medication is usually warranted. But many Dr's will NOT prescribe medicine because you are "normal". Which leads many, many people to remay feeling like crap!
So just because your FT4 and FT3 are "in range" does NOT at all mean that they are adequate. And if you are hypo symptomatic AND your TT3 is low, it would supply some indication that you are infact hypo. Everyone is different and feels well at a different level.
Total T3 is not COMPLETELY useless, it is just not nearly as good as FT3. Just as a fuel gage in a car is not COMPLETLY useless as you do need a supply of gas and knowing that there is fuel in the tank provides SOME information. Just not the entire picture.
Hope this helps.
Please post your blood results and the reference ranges that you have and also your symptoms. With that information we can all help you out the best.
Total T3 is particularly useful in the diagnosis of T3 thyrotoxicosis (single toxic nodule, multinodular thyrotoxicosis, following treatment with T3, occasionally found in Graves' disease).
This lab is recommended for patients with supraventricular tachycardia, fatigue and weight loss not otherwise explained, or for those with proximal myopathy (symmetrical weakness of proximal upper and/or lower limbs) with normal T4 levels.
Reduced total T3 levels can be seen with clinical or subclinical hypothyroidism (1/3rd of hypothyroid patients), starvation, stress, acute illness, certain drugs, reduced levels of thyroid-binding globulin (TBG).
The TT3 test is considered obsolete as a standard test for evaluating thyroid status. TT3 measures the total T3 in the blood. However, much of that TT3 is chemically bound by protein and thus unavailable for the body to use. FT3 measures what is unbound and available, and that's what you want to know. That's what correlates best with symptoms.