For most people, Flicka is right on the money. TSH usually peaks at night after you go to bed. This isn't true for all people, but as a general rule, it is correct.
For T4 levels (and T3 is a similar situation, for people who are taking a med with T3 in it), here is what the online thyroid textbook at [url="http://www.thyroidmanager.org"]www.thyroidmanager.org[/url] says on peak blood levels after taking your meds:
Serum T4 concentrations peak 2 to 4 hours after an oral dose and remain above normal for approximately 6 hours in patients receiving daily replacement therapy. The long half-life of thyroxine of about 7 days allows treatment with a singly daily tablet...
and for you T3 takers:
Liothyronine. After oral administration of L-triiodothyronine sodium (which is more readily absorbed than T4) peak levels of serum T3 are observed within 2 to 4 hours...The half-life of T3 is approximately one day.
In plain English, after you take your pill, your blood level of T3 and/or T4 is artificially high , peaking 2-4 hours after you take the pill and remaining above your base level for 6 hours.
My opinion is that you shouldn't have your blood drawn for about 8 hours after you take your meds if you are having T3 and T4 measured.
If the blood draw is in the morning, wait to take your meds until AFTER the blood draw.
If the blood draw is in the afternoon, schedule it as late as possible and take your meds as early as possible in the morning.
If all you are having done is TSH, my understanding is that TSH is going to be based on your base level, anyways and shouldn't matter on timing in respect to when you took your meds, though it will vary depending on your circadian rhythm.