  A widely accepted phenomenological rule states that solids with free surfaces
cannot be overheated. In this work we discuss this statement critically under
the light of the statistical thermodynamics of interfacial roughening
transitions. Our results show that the basal face of ice as described by the
TIP4P/Ice model can remain mechanically stable for more than one hundred
nanoseconds when overheated by 1~K, and for several hundreds of nanoseconds at
smaller overheating despite the presence of a significant quasi-liquid layer at
the surface. Such time scales, which are often of little experimental
significance, can become a concern for the determination of melting points by
computer simulations using the direct coexistence method. In the light of this
observation, we reinterpret computer simulations of ice premelting and show
that current results for the TIP4P/Ice model all imply a scenario of incomplete
surface melting. Using a thermodynamic integration path, we reassess our own
estimates for the Laplace pressure difference between water and vapor. These
calculations are used to measure the disjoining pressure of premelting liquid
films and allow us to confirm a minimum of the interfacial free energy at
finite premelting thickness of about one nanometer.
