An analysis of the high-multiplicity triggered pp data at $\sqrt{s}$ = 13 TeV, obtained with the ALICE detector, is carried out to study the event-by-event fluctuations of mean transverse momentum ($\langle p_{\rm T}\rangle$) using a two-particle \pt correlator. The driving force behind these studies is the search for dynamical fluctuations that may be associated with the formation of Quark-Gluon Plasma (QGP) droplets in small collision systems, such as pp, for which traces have been observed in previous studies. The values of the correlator are observed to decrease with increasing charged particle density and exhibit power-law behavior similar to the one observed for pp and Pb--Pb collisions at lower energies. The findings also reveal that Monte Carlo model PYTHIA reproduces the observed dependence of the correlator on charged particle density.