The giant flare observed on Dec. 27 ^ { th } 2004 from SGR 1806–20 has revived the idea that a fraction of short ( < 2 s ) Gamma Ray Bursts ( GRBs ) is due to giant flares from Soft Gamma Ray Repeaters located in nearby galaxies . One of the distinguishing characteristics of these events is the thermal ( black body ) spectrum with temperatures ranging from \sim 50 to \sim 180 keV , with the highest temperature observed for the initial 0.2 s spike of the Dec. 27 ^ { th } 2004 event . We analyzed the spectra of a complete sample of short GRBs with peak fluxes greater than 4 photon s ^ { -1 } cm ^ { -2 } detected by BATSE . Of the 115 short GRBs so selected only 76 had sufficient signal to noise to allow the spectral analysis . We find only 3 short GRBs with a spectrum well fitted by a black body , with 60 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } { } kT \lower 2.15 pt \hbox { $ % \buildrel < \over { \sim } $ } 90 keV , albeit with a considerably longer duration ( i.e . \buildrel > \over { \sim } 1 sec ) and a more complex light curve than the Dec. 27 ^ { th } 2004 event . This implies a stringent limit on the rate of extragalactic SGR giant flares with spectral properties analogous to the Dec. 27 ^ { th } flare . We conclude that up to 4 per cent of the short GRBs could be associated to giant flares ( 2 \sigma confidence ) . This implies that either the distance to SGR 1806–20 is smaller than 15 kpc or the rate of Galactic giant flares is lower than the estimated 0.033 yr ^ { -1 } .