A new article has appeared in the journal Thyroid which may be of interest here. First it shows that T3 administration does not return TSH values to the levels seen by using T4. Secondly it shows the "spikes" in T3 that occur over the euthyroid range shortly after taking the dose. The reference is:
J Jonklaas & D Burman
Daily Administration of Short Acting Liothyronine is Associated with Significant Triiodothyronine Excursions and Fails to Alter Thyroid-responsive Parameters (doi: 10.1089/thy.2015.0629)
Again this suggests multiple T3 dosing is safer during the day.