You mentioned that TROs are not appealable, but that preliminary injunctions are.
I realize some of this crosses into appellate procedure, but I'm guessing that TROs are not appealable because they are not final orders of the court.
So how does that differ from a preliminary injunction? "Preliminary" sounds not final, either.
Under 28 U.S.C. § 1292(a), the court of appeals has jurisdiction to review an interlocutory (non-final) order "granting, continuing, modifying, refusing or dissolving injunctions." But because a TRO is not an injunction, § 1292(a) does not permit review.
We get into this in-depth in Federal Courts.