  In the framework of the hypothesis on potential sources of some gamma-ray
bursts being single compact objects of neutron star type with finite surface
temperature in the vicinity of the Sun a method of search in the optical range
for a corresponding candidate in the region of a powerful short burst
localization is considered. The localization region of the GRB790613 event is
studied in the B, V and R filters. B-V and V-R colors of 196 objects with a S/N
> 4 are measured up to the average practical photometric limit B < 25.7, V <
25.7 and R < 25.6 for the whole obtained mosaic of CCD images. No blue objects
with B-V < 0 and V-R <0 were found up to B \approx 25.2, which can be
interpreted as the absence of a compact object with a temperature > 1.5 10^{5},
K in this direction up to a distance \approx 40, pc. A probable common upper
limit to the temperature of the supposed compact objects in the vicinity of the
Sun is indicated based on the accumulated optical and X--ray data. The study of
blue (B-V < 0) objects in the smallest (in the northern sky) gamma-ray box
GRB790613, in view of the results of the search for point-like sources in the
soft X--ray in the localization regions of bright gamma-ray bursts, does not
exclude the existence of such ``cold'' (<= 10^{5} K) objects, which could give
an essential contribution to the observed density of hidden matter close to the
Sun and some of them could be related with the closest sources of gamma-ray
bursts. Several interesting objects were also found in (or near) the
localization region of the GRB790613 event.
