Here is a very recent case study article showing the need to take care in storing T4 tablets. It's one more thing to look out for, but I would think that only rarely would someone routinely mis-store tablets.
CASE REPORT ARTICLE
Front. Endocrinol., 10 July 2017 | doi.org/10.3389/fendo.2017....
Refractory Hypothyroidism Due to Improper Storage of Levothyroxine Tablets
Salvatore Benvenga, Giampaolo Papi and Alessandro Antonelli
The article is easily available for anyone interested - just go to Articles in the site "Frontiers in Thyroid Endocrinology".