DNP will suppress T3 levels. That is both good and bad.
Good: that means it is not very catabolic. Suppression of T3 is what helps make DNP so muscle-sparing.
Bad: T3 levels, of course, take a little while to recover. Fortunately, T3 appears to recover faster from DNP suppression than from the suppression that results due to T3 supplementation.
I'd suggest following a DNP cycle with a stack of Guggulbolics and MM4 from Syntrax, which both naturally stimulate the thyroid into recovery.