The half-life of T3 is less than a day. That means you will reach full effect of a dosage change on serum levels in about 5 days. T4 has a half-life of about one week. So it takes about 5 weeks to get to over 95% of the final effect on serum levels.
If however, you are talking about the effect on symptoms that is a different matter. Symptoms tend to lag somewhat behind changes in serum levels of thyroid hormone.