This paper using rats shows that T2 in substantial amounts can both stimulate body metabolism and also exert an effect on the pituitary to give central hypothyroidism. No doubt we humans never achieve that level of T2 but the paper serves as a warning over too much T2 in the body. It's open access
Administration of 3,5-diiodothyronine (3,5-T2) causes central hypothyroidism and
stimulates thyroid-sensitive tissues
Alvaro Souto Padron, Ruy Andrade Louzada Neto, Thiago Urgal Pantalea, Maria Carolina de Souza dos Santos, Renata Lopes Araujo, Bruno Moulin de Andrade, Monique da Silva Leandro, Joa˜o Pedro Saar Werneck de Castro, Andrea Claudia Freitas Ferreira and Denise Pires de Carvalho
joe.endocrinology-journals.org
DOI: 10.1530/JOE-13-0502