  We show that the introduction of thermal noise in Invasion Percolation (IP)
brings the system outside the critical point. This result suggests a possible
definition of SOC systems as ordinary critical systems where the critical point
correspond to set to 0 one of the parameters. We recover both IP and EDEN
model, for $T \to 0$, and $T \to \infty$ respectively. For small $T$ we find a
dynamical second order transition with correlation length diverging when $T \to
0$.
