The only evidence at all for a dietary cause of hypothyroidism is an iodine deficiency.
Pretty sure there is more evidence than just iodine. Just to mention three: protein amount and proportion of the diet, polyunsaturated fats, and magnesium.
For example, protein deficiency slows down metabolism. Just see what difference in pulse and temperature you get (because it's easier to measure) by taking 20 grams of protein per day, 40 grams, 60 g, 80g, and 100 g.
There are studies about using different oils, the more polyunsaturated oils produce more weight gain. This is consistent with animal studies showing polyunsaturated fats slow down the metabolic rate.
Magnesium supplements reduce TSH, which likely means it increases the metabolic rate.
I'm sure you can find many other things. It would be harder to find something that does not affect the metabolic rate.