  The first measurements of skewness and kurtosis of mean transverse momentum
($\langle p_\mathrm{T}\rangle$) fluctuations are reported in Pb$-$Pb collisions
at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV, Xe$-$Xe collisions at
$\sqrt{s_\mathrm{NN}}$ $=$ 5.44 TeV and pp collisions at $\sqrt{s} = 5.02$ TeV
using the ALICE detector. The measurements are carried out as a function of
system size $\langle
\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle_{|\eta|<0.5}^{1/3}$, using
charged particles with transverse momentum ($p_\mathrm{T}$) and pseudorapidity
($\eta$), in the range $0.2 < p_\mathrm{T} < 3.0$ GeV/$c$ and $|\eta| < 0.8$,
respectively. In Pb$-$Pb and Xe$-$Xe collisions, positive skewness is observed
in the fluctuations of $\langle p_\mathrm{T}\rangle$ for all centralities,
which is significantly larger than what would be expected in the scenario of
independent particle emission. This positive skewness is considered a crucial
consequence of the hydrodynamic evolution of the hot and dense nuclear matter
created in heavy-ion collisions. Furthermore, similar observations of positive
skewness for minimum bias pp collisions are also reported here. Kurtosis of
$\langle p_\mathrm{T}\rangle$ fluctuations is found to be in good agreement
with the kurtosis of Gaussian distribution, for most central Pb$-$Pb
collisions. Hydrodynamic model calculations with MUSIC using Monte Carlo
Glauber initial conditions are able to explain the measurements of both
skewness and kurtosis qualitatively from semicentral to central collisions in
Pb--Pb system. Color reconnection mechanism in PYTHIA8 model seems to play a
pivotal role in capturing the qualitative behavior of the same measurements in
pp collisions.
