I am a little late getting to the paper published by Begoña Ruiz-Núñez and colleagues  observing that, at least for some diagnosed with chronic fatigue syndrome (CFS), clinical findings related to thyroid function might "resemble a mild form of “non-thyroidal illness syndrome” and “low T3 syndrome” experienced by a subgroup of hypothyroid patients receiving T4 monotherapy." But I did get here eventually. Before heading into this paper, I'm gonna link to one of the 'already prepared' discussions on the Ruiz-Núñez findings (see here). My analysis is pretty similar but not entirely the same...
So: "We studied 98 CFS patients (21–69 years, 21 males) and 99 age- and sex-matched controls (19–65 years, 23 males)" was the starting point, as participants provided blood samples and 24-hour urine samples onward to various analyses being carried out. This included: "the measurement of routine hematological parameters [Hb, hematocrit, WBC, red blood cells (RBC), and thrombocytes]" and more specifically: "parameters of thyroid function, low-grade inflammation and gut wall integrity..., together with secondary markers of inflammation." Those 'parameters of thyroid function' included various measures of free and total levels of T3 and T4 required to ascertain the presence of "low-T3 syndrome." I was impressed to see that a measure of gut wall integrity was also on the research menu in the form of plasma zonulin levels being included (albeit analysed via ELISA and bearing in mind the issues that have emerged with that particular method).
Results: "Chronic fatigue syndrome patients exhibited lower FT3, TT4, TT3, %TT3, SPINA-GD, and SPINA-GT, lower ratios of TT3/TT4, FT3/FT4, TT3/FT3, and TT4/FT4; and higher %rT3 and rT3/TT3 ratio." These findings were based on 'group' comparisons with those sex-matched not-CFS controls, and point to some 'issues' with thyroid function in general. Coupled to other thyroid related findings, the Ruiz-Núñez suggest that lower levels of thyroid hormones were detected but "distinct from thyroidal disease" typical levels of thyroid-stimulating hormone (TSH) were also reported. TSH is the stuff that tells the thyroid gland to make thyroid hormone (thyroxine (T4)), where T4 is, in effect, the starting material for T3 (triiodothyronine). Where there are suitable levels of TSH but lower levels of T4 and/or T3, one gets the impression that it's more about what's 'happening' to T3 and T4 over and above issues with their production. Indeed, the collected findings led authors to talk about that 'low T3 [triiodothyronine]syndrome' as being potentially pertinent to their findings in relation to CFS. Going back to those plasma zonulin findings, and there is just a sentence from Ruiz-Núñez and colleagues: "Zonulin, a parameter of intestinal permeability... was lower in CFS patients as compared to controls" but not much else.
I'm not particularly au fait with all the details of low T3 syndrome in the context of CFS or anything else so can't really add too much more. From what I gather, this is not a CFS-exclusive condition but does seemingly tap into talk about CFS being reflective of a "hypometabolic state" (see here). Questions about how to 'treat' such thyroid-related issues in the context of CFS remain unanswered, despite authors talking about "trials with, e.g., T3 and iodide supplements" being potentially indicated. I say this bearing in mind that the focus on biochemistry in the Ruiz-Núñez paper could perhaps, have been complemented by a little more on the presentation of clinical symptoms too.
In short, quite a bit more investigation in this area is indicated...
 Ruiz-Núñez B. et al. Higher Prevalence of “Low T3 Syndrome” in Patients With Chronic Fatigue Syndrome: A Case–Control Study. Front. Endocrinol. 2018. Mar 20.