  Inelastic electron tunneling and surface-enhanced optical spectroscopies at
the molecular scale require cryogenic local temperatures even under
illumination - conditions that are challenging to achieve with plasmonically
resonant metallic nanostructures. We report a detailed study of the laser
heating of plasmonically active nanowires at substrate temperatures from 5 to
60 K. The increase of the local temperature of the nanowire is quantified by a
bolometric approach and could be as large as 100 K for a substrate temperature
of 5 K and typical values of laser intensity. We also demonstrate that a $\sim
3\times$ reduction of the local temperature increase is possible by switching
to a sapphire or quartz substrate. Finite element modeling of the heat
dissipation reveals that the local temperature increase of the nanowire at
temperatures below $\sim$50 K is determined largely by the thermal boundary
resistance of the metal-substrate interface. The model reproduces the striking
experimental trend that in this regime the temperature of the nanowire varies
nonlinearly with the incident optical power. The thermal boundary resistance is
demonstrated to be a major constraint on reaching low temperatures necessary to
perform simultaneous inelastic electron tunneling and surface enhanced Raman
spectroscopies.
