  We study the stability of a Bose condensate of atomic $^7$Li in a (harmonic
oscillator) magnetic trap at non-zero temperatures. In analogy to the stability
criterion for a neutron star, we conjecture that the gas becomes unstable if
the free energy as a function of the central density of the cloud has a local
extremum which conserves the number of particles. Moreover, we show that the
number of condensate particles at the point of instability decreases with
increasing temperature, and that for the temperature interval considered, the
normal part of the gas is stable against density fluctuations at this point.
