  Distinct works have claimed that spatial (quenched) disorder can suppress the
discontinuous absorbing phase transitions. Conversely, the scenario for
temporal disorder for discontinuous absorbing phase transitions is unknown. In
order to shed some light in this direction, we tackle its effect in three
bidimensional examples, presenting undoubtedly discontinuous absorbing phase
transitions. Except in one case (to be explained further), the temporal
disorder is introduced by allowing the control parameter to be time dependent
$p\rightarrow p(t)$ according to a uniform distribution of mean $p_0$ and width
$\sigma$, in which at the emergence of the phase transition the system transits
between active and absorbing regimes. In contrast to the spatial disorder,
numerical results strongly suggest that temporal disorder does not forbid the
existence of discontinuous transition. All cases are signed by behaviors
similar to their pure (without disorder) counterparts, including bistability
around the coexistence point and common finite size scaling behavior with the
inverse of the system volume, as recently proposed in Phys. Rev. E. {\bf 92},
062126 (2015). We also observe that temporal disorder does not induce temporal
Griffiths phases around phase transitions, at least for $d=2$.
