Peat is very skeptical to the thyroid lab tests to begin with, probably for good reason. "Normal" free T3 is not a sign that things are the way they should. But if you have a consistently low free T3, it is a sign something is definitely wrong. I had way low free T3 for seven months before starting desiccated thyroid.
Measuring heart rate, taking temperature and monitor other symptoms is important - more important than lab tests. I even have the GD hammer.
I was following the Total T3 measurement philosophy for a while (as recommended by one of the Paleo "guru" clinicians). But as I was not getting any results with his focus on reverse T3, I eventually started reading Peat. This led me to understand that my problem was the conversion of T4 to active thyroid hormone in the liver. This has several very practical applications. The reverse T3 focus for me left more questions than answers. What´s the practical implications of the hypothesis that your problem is high reverse T3? Take pure T3 instead of desiccated? Maybe - but I have seen people focusing on reverse T3 do that, and then having better results with desiccated. Anyway, I see that Peat mention Total T3 a couple of places. Maybe it can be helpful for some people.
Anyway, for many women, I think the focus on improving conversion of T4 to T3 is very helpful - focusing on the liver: reducing excess estrogen, supplying glucose to liver cells, trying to increase glycogen stores in muscles and liver etc.
For me, I have to say there has been a significant correlation between free T3 lab test results and other symptoms of too little active thyroid hormone. One example: in December I started to feel a bit crappy again. Low energy, sleep deteriorated, feeling of rapid and heavy heart beat (adrenaline) etc. My morning waking HR was 39 (yes, I am not exaggerating). My morning temperature was stable, but that has been the case with me - temps have had limited diagnostic value, very consistent. Anyway, I had a free T3 test, and rightly, it had dropped below the lab range again.
Another note on lab tests: they vary significantly from lab to lab, so don´t take one test results as something absolute. One example: when I first started having symptoms, I got a doctor to prescribe several tests for me, including anti-bodies associated with both hyper and hypo. To get these he had to send my blood to two different labs - the top hospital for hormonal diseases and the best private lab in my native country (Europe). For some reason, he asked both labs to test Free T3. The blood was drawn at the exact same time. The free T3 results were significantly different. One lab measured free T3 to be below their lab range. The other came out lower middle, within the normal functional range.