I am wondering if someone could help me.

Firstly does anyone know if thyroid (TSH, T3, T4) have pulsatile or cicadian rhythms such as cortisol has? I seem to have the impression that it does but am finding it hard to find information indicating such. Also if there is a chart out there which shows these rhythms and the timing of normal thyroid secretion that would be particularly good. 

Also does anyone know whether there is a negative clash of medication if one takes thyroid replacement at the same time as hydrocortisone replacement? I have had contradictory advice on this and would like to clarify.