  Next generation of cosmological observations are expected to improve the
measurements of several quantities connected to the primordial inflation in the
early Universe. These quantities include for example improved measurements for
the spectral index of the scalar curvature of the primordial power spectrum and
to also bring a better understanding on the scaling dependence of the
primordial spectrum. This includes the running of the tilt and, possibly, also
the running of the running. In this paper, we investigate the possibility of
generating large runnings in the context of warm inflation. Useful analytical
expressions for the runnings are derived in the context of warm inflation in
the strong dissipation regime. The results are compared to and discussed for
some well motivated primordial inflaton potentials that have recently been of
interest in the literature.
