  In the context of thermodynamics applied to our cosmological apparent
horizon, we explicit in greater details our previous work which established the
Friedmann Equations from projection of Hayward's Unified First Law. In
particular, we show that the dynamical Hayward-Kodama surface gravity is
perfectly well-defined and is suitable for this derivation. We then relate this
surface gravity to a physical notion of temperature, and show this has
constant, positive sign for any kind of past-inner trapping horizons. Hopefully
this will clarify the choice of temperature in a dynamical
Friedmann-Lema\^itre-Roberston-Walker spacetime.
