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We present a study of the effects of temperature upon the excitationfrequencies of a Bose-Einstein condensate formed within a dilute gas with aweak attractive effective interaction between the atoms. We use theself-consistent Hartree-Fock Bogoliubov treatment within the Popovapproximation and compare our results to previous zero temperature andHartree-Fock calculations The metastability of the condensate is monitored bymeans of the $l=0$ excitation frequency. As the number of atoms in thecondensate is increased, with $T$ held constant, this frequency goes to zero,signalling a phase transition to a dense collapsed state. The critical numberfor collapse is found to decrease as a function of temperature, the rate ofdecrease being greater than that obtained in previous Hartree-Fockcalculations.Comment: 4 pages LaTeX, 3 eps figures. To appear as a letter in J. Phys.

Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions