Our foxers always puffed their coats during their spring molt, when temperatures vary.
As far as thyroid function goes, if the diet is high in uncooked Brassica greens and stalked vegetables, soymeal, yams, cassava, etc. that contain higher amounts of 'goitrogenic' compounds that negatively impact the function of the parathyroid gland, this can lend to the development of obesity.
Thankfully boiling the greens deactivates most of the 'goitrogens' that they contain. For soymeal in block the only option to remove soy from the diet is to switch to a block that doesn't contain soymeal, like HHB, or the Envigo HT 2016 global rodent diet.
Our female foxer loved the block a bit too much as an adult and became grossly obese compared to our other girl. Exercise didn't seem to help either. Sadly we didn't know then about these compounds in common foods as we do now.
https://www.healthline.com/nutrition...foods#section3