You would get much greater benefit if you took the T3 longer than 3 weeks.
And yes, it is plenty safe to run T3 longer than 3 weeks.
Actually the half life of T3 is 2.5 days:
Since liothyronine sodium (T3) is not firmly bound to serum protein, it is readily available to body tissues. The onset of activity of liothyronine sodium is rapid, occurring within a few hours. Maximum pharmacologic response occurs within 2 or 3 days, providing early early response. The biological half-life is about 2.5 days.
http://dailymed.nlm.nih.gov/dailymed...o.cfm?id=10973