Do you have low T3? If so, then it is likely that you also have some of the standard hypothyroid symptoms: lowered testosterone, decreased libido, mental fog, fatigue and perhaps decreased erectile strength. Some physicians will immediately put you on thyroid medications. The good news is that thyroid meds appear to be quite safe and pretty easy to quit, unlike many other pharmaceuticals. However, wouldn't you like to know the root cause of your low T3 if at all possible? Why spend the time and money on medications if you don't have to, eh? What has happened is that the research that has been pouring out of the laboratories has just not made it into the doctor's offices yet. It will happen, but natural solutions are just not considered yet.
Before I discuss those solutions, I want to answer a question that may have crossed your mind: why am I only focusing on T3 in this article. After all, low T3 men tend to fall in one of two categories: a) medium high T4, low T3 or b) low T3 and low T4. And the T4 level does provide valuable information actually. For example, if you have low T4, it is possible that you have a damaged pituitary - the pituitary actually sends the signal to the thyroid to produce T3 and T4 -or that your thyroid is under autoimmune attack, etc. (You can read about some of the other reasons for hypothyroidism and how it can affect testosterone on this page: Testosterone and Your Thyroid.)
But, again, on this page I want to cover lifestyle and chronic disease-related issues that may help you to reverse, partially or otherwise your hypothyroidism. And this is important, because, if you have an underlying lifestyle issues, it is probably causing you other problems that you may not even be aware of. That's why I believe it is important to read some of these Less Well Known and Potentially Correctiale Reasons for Low T3:
1. Low Zinc. According to an animal study, low zinc levels could lead to decreased T4, which, in turn, could lead to decreased T3 levels.  Zinc deficiencies can also dramatically affect testosterone levels as I discuss in my page on Zinc Deficiencies and Low Testosterone. One way to test for a zinc deficiency is through a simple zinc taste test. CAUTION: Be sure to ready my page on The Nasty Effects of Too Much Zinc.
2. Magnesium Deficiency. Zinc isn't the only mineral that can sometimes lower testosterone: there is evidence that magnesium deficiencies can do the same thing. And so is it any wonder that low magnesium can also lower thyroid hormones as well? An animal study shows that this is exactly what happens: magnesium deficient animals had decreased T4 output, increased TSH and their thyroid gland enlarged.  And studies have shown that many individuals are walking around with low levels of magnesium. The reasons are many, but at the top of the list are probably the fact that magnesium-rich foods are avoided by some men andsoils are now often depleted
3. Dieting. A lot of men don't realize that, if they significantly cut calories, it will lower testosterone and push them into a state of hypothyroidism. Basically, the body slows down to conserve energy. It's hard to fight Mother Nature!
4. Stress. One study deliberately put men in a stressful combat training situation and found that T3 levels did not decrease significantly. However, what did decrease was free T3, the bioactive T3 needed by your tissues.  Interestingly enough, the researchers did not find increased stress hormone levels in these men, but the fact reamins that their free T3 was somehow affected.
5. Selenium Deficiency. It's not just magneisum - soils are often depleted of selenium now as well.  This can negatively impact thyroid function, because selenium is a key part of certain thyroid enzymes and is needed for the conversion of T4 into T3.  As expected, animals studies show decreased thyroid output from low selenium.  You can get a beefy does of selenium in brazil nuts, but be careful: do not eat more than one per day and that may even be too much. You can actually poison yourself with selenium as the typical brazil nut has an RDA or two in it.
6. Riboflavin (Vitamin B2) and Pryidoxine (Vitamin B6). One study showed that low levels of Vitamin B2 led to decreased conversion to T3.  And too little Vitamin B6 can rev up your immune system, such that it attacks the thyroid.
7. Tyrosine Deficiency. Some people do not make enough tyrosine from phenylalanine due to an enzyme deficiency. This is quite rare though. However, there is a theory out there that, under stress, we need more tyrosine, perhaps even supplemental. I have no studies to show tyrosine supplementation helped T3 levels but am just passing along information.
8. Gut Issues. Many men walk around with diarrhea, constipation, intestinal cramping, etc. and do not realize that they are part of the epidemic of gut issues that includes Crohn's, Irritable Bowel Syndrome, Diverticulitis, Celiac Disease and many more. These gut issues have massive counterintuitive consequences and one of them is decreased nutrient absorption. Yes, that means that it is quite common for men with these diseases to have low levels of all the nutrients and vitamins that you see above.
Stomach issues are quite prevalent and can cause similar nutrient-absoprtion issues as well. Atrophic gastritis is prime example: you have to give good stomach acid to aid those chemical reactions in your stomach. So, if you have any doubts about the health of your GI tract, get checked asap.
9. Inflammation and Infection. Many lines of evidence have pointed to inflammation lowering thyroid hormones. To test this theory out, researchers built an elaborate animal model and discoverd that both T3 and T4 were lowered by inflammation. 
1) Biological Trace Element Research, Jan 1998, 61(1):89-96, "Zinc supplementation on serum levels and hepatic conversion of thyroid hormones in obese (ob/ob) mice
2) The Journal of Nutrition, 1984, 114(8):1510-1517, "The effect of magnesium depletion on thyroid function in rats"
3) Life Sciences, 1994, 55(17):PL327 PL332, "Impact of stress and triiodothyronine on plasma magnesium fractions"
4) Endocrinology, 2000 Jul, 141(7):2490-500, "Effects of selenium deficiency on tissue selenium content, deiodinase activity, and thyroid hormone economy in the rat during development.
5) Am J Clin Nutr, 1993 Feb, 57(2 Suppl):236S-239S, "Selenium deficiency, thyroid hormone metabolism, and thyroid hormone deiodinases"
7) J Endocrinol, Dec 1 2006, 191:707-714, "Chronic local inflammation in mice results in decreased TRH and type 3 deiodinase mRNA expression in the hypothalamic paraventricular nucleus independently of diminished food intake"
8) Endocrinology, Published Online: July 01, 2013, "Effects of Vitamin Deficiency on the in Vitro and in Vivo Deiodination of Thyroxine in the Rat"