  Driven many-body systems typically experience heating due to the lack of
energy conservation. Heating may be suppressed for time-periodic drives, but
little is known for less regular drive protocols. In this work, we investigate
the heating dynamics in aperiodically kicked systems, specifically those driven
by quasi-periodic Thue-Morse or a family of random sequences with
$n$-multipolar temporal correlations. We demonstrate that multiple heating
channels can be eliminated even away from the high-frequency regime. The number
of eliminated channels increases with multipolar order $n$. We illustrate this
in a classical kicked rotor chain where we find a long-lived prethermal regime.
When the static Hamiltonian only involves the kinetic energy, the prethermal
lifetime $t^*$ can strongly depend on the temporal correlations of the drive,
with a power-law dependence on the kick strength $t^*\sim K^{-2n}$, for which
we can account using a simple linearization argument.
