  We investigate theoretically a one-dimensional ideal Bose gas that is driven
into a steady state far from equilibrium via the coupling to two heat baths: a
global bath of temperature $T$ and a "hot needle", a bath of temperature
$T_h\gg T$ with localized coupling to the system. Remarkably, this system
features a crossover to finite-size Bose condensation at temperatures $T$ that
are orders of magnitude larger than the equilibrium condensation temperature.
This counterintuitive effect is explained by a suppression of long-wavelength
excitations resulting from the competition between both baths. Moreover, for
sufficiently large needle temperatures ground-state condensation is superseded
by condensation into an excited state, which is favored by its weaker coupling
to the hot needle. Our results suggest a general strategy for the preparation
of quantum degenerate nonequilibrium steady states with unconventional
properties and at large temperatures.
