Sounds logical, and that's what Dr. Phinney says they saw.
Interestingly, Jack Kruse is saying that upping your carbohydrate level will raise T3, but that so will eating a low-carbohydrate diet, so long as it has sufficient iodine in it. This means seafood. He says what most people in paleo have missed is that we evolved in the Rift Valley and there would have been plenty of water-resources there. (I think his references do, indeed, sustain that. But they'd not be alone: Raymond Dart, and hence a lot people who accepted his general picture, missed that, too.)
It's interesting stuff, though seemingly not congruent with what Phinney says they saw.
Anyway, Jack's solution seems to be to eat carbs in the summer when they're there, but to go ketogenic (and particularly heavy on the seafood -- as the traditional saying has it, "oysters when there's a R in the month"[*] ) in the winter. And that probably gives the best match for circadian rhythms, anyway.
BRAIN GUT 12: DARE TO DISAGREE? | Jack Kruse
I always quite liked that solution when it was offered in
Lights Out. It seems to make sense at a lot of levels.
Of course, people whose metabolism would seem basically to be broken, like Jimmy Moore, are probably sensible to go ketogenic regardless of seasonality.
__________________________[*] That was actually probably because they more likely to be off in the warmer months, and is probably a reflection on how careless people were about keeping inshore waters clean in the last couple of hundred years.