  We explore the warm inflation scenario theoretical predictions looking at two
different dissipative regimes for several representative primordial potentials.
As it is well known, the warm inflation is able to decrease the
tensor-to-scalar ratio value, rehabilitating several primordial potential ruled
out in the cold inflation context by the recent cosmic microwave background
data. Here we show that it is also able to produce a running of the running
$n_s"$ positive and within the Planck data limits. This is very remarkable
since the standard cold inflation model is unable to justify the current
indication of a positive constraint on $n_s"$. We achieve a parameterization
for the primordial power spectrum able to take into account higher order
effects as the running of the spectral index and the running of the running,
and we perform statistical analysis using the most up-to-date Planck data to
constrain the dissipative effects. We find that the warm inflation can explain
the current observables with a good statistical significance, even for those
potentials ruled out in the simplest cold inflation scenario.
