I'd start at 25mcg/day, but split it up in three doses. T3 is short lived in the body. Basically, by dosing t3 for this condition, you are manually controlling the throttle on your metabolism.

When you exercise, or cause any increase in activity, your thyroid gland is SUPPOSED to respond and up the levels of free t3 to match what your body needs. So if you're going to do something like cardio, lifting, etc. you have to take your t3.

Right now I wake up, dose 20mcg t3, lay there for fifteen minutes and then start drinking bcaa's and water. Half an hour later, i'm at the gym doing cardio for 30mins-2hrs. Lately i've been upping the cardio.
Half way through, i'll drink a protein isolate shake...25g or so. Post work out, i'll do the same thing. Generally, when I dose t3, I try to make sure that immediately after I take it, I get some sort of aminos in my body to prevent any bit of catabolism caused by t3.

Through out the rest of the day, i make sure I'm getting a total of 200-250g protein, around 100g complex carbs, and 1tbsp olive oil. 1500cal total per day. On HIIT days, I'll add about 50g carbs post work out.

I try to spread my t3 out as much as possible. Right now i'm trying to stick to around 80mcg total/day...but i'm feeling like it might be more than I need. Once I get my dessicated thyroid from Thailand (contains T1, T2, T3, T4, calcitonin) I will be switching to that. It's closer to what the body actually needs. I've found that by suppressing my natural production of thyroid hormones, whatever was being produced feels like it's shut down at this point. My mood swings are back but not as severe, as well as the other issues such as poor circulation, cold sweaty feet, and dry skin. I take my temperature through out the day, and try to dose accordingly and keep myself in the 97.8-99 range. Normally when I wake up w\o t3 overnight, I will be at about 95. (biggest sign of hypothyroidism)

The weight loss is working at the rate it should, so I am at least semi-happy for the time being.

I leave my t3 at room temperature in a dark drawer to prevent it from going bad. I leave it under my tongue for 3-5 mins then swallow. As a general rule, take it on an empty stomach.