  This work reports the dynamical thermal behavior of lasing microspheres
placed on a dielectric substrate while they are homogeneously heated-up by the
top-pump laser used to excite the active medium. The lasing modes are collected
in the far-field and their temporal spectral traces show characteristic
lifetimes of about 2 ms. The latter values scale with the microsphere radius
and are independent of the pump power in the studied range. Finite-Element
Method simulations reproduce the experimental results, revealing that the
thermal dynamics is dominated by the heat dissipated towards the substrate
through the medium surrounding the contact point. The characteristic system
scale regarding thermal transport is of few hundreds of nanometers, thus
enabling an effective toy model for investigating heat conduction in
non-continuum gaseous media and near-field radiative energy transfer.
