  We study the hot medium effects in high-multiplicity proton-proton (pp)
collisions at $\sqrt{s_{NN}}=13$ TeV via the charmonium probes. The hot medium
is described with the hydrodynamic model, while charmonium evolutions in the
medium are studied with a time-dependent Schr\"odinger equation. The hot medium
dissociation on charmonium is considered with the temperature-dependent complex
potential parametrized with the results from lattice QCD calculations. The
ratio $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ of $J/\psi$ and $\psi(2S)$ production
cross sections are calculated and compared with the LHCb experimental data in
pp collisions. Our calculations explain the charmonium relative suppression in
different transverse momentum and multiplicity bins. The suppression of this
ratio is mainly affected by the effects of the deconfined medium. It is less
affected by the initial effects before the generation of the heavy quark pair.
We suggest this to be a clear signal of the small QGP droplets generated in
high multiplicity pp collisions.
