The $Lambda$CDM prediction of $S_8equivsigma_8(Omega_m/0.3)^{0.5}$ -- where $sigma_8$ is the root mean square of matter fluctuations on a 8 $h^{-1}$Mpc scale -- once calibrated on Planck CMB data is $2-3sigma$ lower than its direct estimate by a number of weak lensing surveys. In this paper, we explore the possibility that the $S_8$-tension is due to a non-thermal hot dark matter (HDM) fractional contribution to the universe energy density leading to a power suppression at small-scales in the matter power spectrum. Any HDM models can be characterized by its effective mass $ m_{sp}^{rm eff}$ and its contribution to the relativistic degrees of freedom at CMB decoupling $Delta N_{rm eff}$. Taking the specific example of a sterile particle produced from the decay of the inflaton during a matter dominated era, we find that from Planck only the tension can be reduced below $2sigma$, but Planck does not favor a non-zero ${m_{sp}^{rm eff},Delta N_{rm eff}}$. In combination with a measurement of $S_8$ from KIDS1000+BOSS+2dfLenS, the $S_8$-tension would hint at the existence of a particle of mass $ m_{sp}^{rm eff} simeq 0.67_{-0.48}^{+0.26}$ ${rm eV}$ with a contribution to $Delta N_{rm eff} simeq0.06pm0.05$. However, Pantheon and BOSS BAO/$fsigma_8$ data restricts the particle mass to $m_{sp}^{rm eff} simeq 0.48_{-0.36}^{+0.17}$ and contribution to $Delta N_{rm eff} simeq 0.046_{-0.031}^{+0.004}$. We discuss implications of our results for other canonical non-thermal HDM models -- the Dodelson-Widrow model and a thermal sterile particle with a different temperature in the hidden sector. We report competitive results on such hidden sector temperature which might have interesting implications for particle physics model building, in particular connecting the $S_8$-tension to the longstanding short baseline oscillation anomaly.
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