If you take a T4 or T3 drug and tend toward the hypo side, the answer is Yes. Take selenium. It will help your body make better use of the thyroxine.
Take it at least 4 hours after the thyroxine.
The RDA is around 70mcg I believe so don't overdo it. Selenium is widely available in a 200mcg pill so it is probably safe to take that much. To be on the safe side I break the 200mcg pills in half and take 100mcg per day, a little more than the RDA.
My body was very slow to reap the benefits of my Synthroid when I first started taking it. It may be just a coincidence but I noticed a big improvement not long after I added selenium to my supplement routine.
I take 100mg a day. As well as helping convert T4 to T3 it also helps with depression -
Psychopharmacology (Berl). 1990;102(4):549-50.
Selenium supplementation improves mood in a double-blind crossover trial.
Benton D, Cook R.
Department of Psychology, University College, Swansea, Wales, UK.
The possibility that a sub-clinical deficiency of the trace element selenium might exist in a sample of the British population was examined by giving a selenium supplemented for 5 weeks. Using a double-blind crossover design 50 subjects received either a placebo or 100 micrograms selenium on a daily basis. On three occasions they filled in the Profile of Moods state. Mood did not change when taking the placebo, whereas when taking the selenium the subjects reported a substantial improvement after both 2.5 and 5 weeks.