  Control of cooling and heating processes is essential in many industrial and
biological processes. In fact, the time evolution of an observable quantity may
differ according to the previous history of the system. For example, a system
that is being subject to cooling and then, at a given time $t_{w}$ for which
the instantaneous temperature is $T(t_w)=T_{\mathrm{st}}$, is suddenly put in
contact with a temperature source at $T_{\mathrm{st}}$ may continue cooling
down temporarily or, on the contrary, undergo a temperature rebound. According
to current knowledge, there can be only one "spurious" and small peak/low.
However, our results prove that, under certain conditions, more than one
extremum may appear. Specifically, we have observed regions with two extrema
and a critical point with three extrema. We have also detected cases where
extraordinarily large extrema are observed, as large as the order of magnitude
of the stationary value of the variable of interest. We show this by studying
the thermal evolution of a low density set of macroscopic particles that do not
preserve kinetic energy upon collision, i.e., a granular gas. We describe the
mechanism that signals in this system the emergence of these complex and large
memory effects, and explain why similar observations can be expected in a
variety of systems.
