  Energetic feedback processes during the formation of galaxy clusters may have
heated and ionized a large fraction of the intergalactic gas in proto-cluster
regions. When such a highly ionized hot ``super-bubble'' falls along the
sightline to a background quasar, it would be seen as a large void, with little
or no absorption, in the Lyman alpha forest. We examine the spectra of 137
quasars in the Sloan Digital Sky Survey, to search for such voids, and find no
clear evidence of their existence. The size distribution of voids in the range
5-70 Angstrom (corresponding to physical sizes of approximately 3-35 comoving
Mpc/h) is consistent with the standard model for the Lyman alpha forest without
additional hot bubbles. We adapt a physical model for HII bubble growth during
cosmological reionization (Furlanetto, Zaldarriaga and Hernquist 2004), to
describe the expected size-distribution of hot super-bubbles at redshift around
z = 3. This model incorporates the conjoining of bubbles around individual
neighboring galaxies. Using the non-detection of voids, we find that models in
which the volume filling factor of hot bubbles exceeds approximately 20 percent
at z=3 can be ruled out, primarily because they overproduce the number of large
(40-50 Angstrom) voids. We conclude that any pre-heating mechanism that
explains galaxy cluster observations must avoid heating the low-density gas in
the proto-cluster regions, either by operating relatively recently (z<3) or by
depositing entropy in the high-density regions.
