We investigate theoretical and observational aspects of a warm inflation
scenario driven by the $\beta $ -exponential potential, which generalizes the
well-known power law inflation. In such a scenario, the decay of the inflaton
field into radiation happens during the inflationary phase. In our study, we
consider a dissipation coefficient ($\mathrm{\Gamma}$ ) with cubic dependence on the
temperature ($T$ ) and investigate the consequences in the inflationary
dynamics, focusing on the impact on the spectral index ${n}_{s}$ , its running
${n}_{run}$ and tensor-to-scalar ratio $r$ . We find it possible to realize
inflation in agreement with current cosmic microwave background data in weak
and strong dissipation regimes. We also investigate theoretical aspects of the
model in light of the swampland conjectures, as warm inflation in the strong
dissipation regime has been known as a way to satisfy the three conditions
currently discussed in the literature. We find that when $\mathrm{\Gamma}\propto {T}^{3}$ ,
the $\beta $ -exponential model can be accommodated into the conjectures.