  Galileon models are among the most appealing candidates for Dark Energy. The
reason is twofold: classically, they provide a tracking solution leading to an
almost DeSitter space starting from very generic initial conditions in the deep
radiation era. The second reason is the standard lore that Galileons are
quantum mechanically stable. The latter property is certainly true in flat
space-time, thanks to the non-renormalization theorems of galilean coupling
constants. However, in a cosmological background, we show that quantum effects
might dominate the classical trajectory. Assuming the radiation era to last at
least up to the electroweak phase transition, the trajectory with initial
conditions sitting on the tracker is ruled out. On the other hand, it is always
possible to find a sub-space of initial conditions such that the dark energy
solution approaches stably the tracker at late times. Fixing the value of
initial conditions that best fit current data, and assuming that the galileon
effective theory is valid up to the beginning of the radiation epoch, we found
that the reheating temperature of the universe cannot be larger than $10^8 \
{\rm GeV}$. Reversing the argument, if dark energy will turn out to be in form
of Galileons, the bounds by EUCLID on the initial conditions for these models
will also be a bound on the reheating temperature of our Universe.
