  We consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the
Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x
-y))$. We prove that the thermal equilibrium at low temperatures exhibits the
Bose-Einstein condensation in a strong sense, namely the probability of having
$n$ particles outside of the condensation decays exponentially in $n$.
