  We study the evolution with temperature of quasiparticle bound states around
non-magnetic impurities in d-wave superconductors. The associated local density
of states has a fourfold symmetry which has recently been observed in Zn-doped
Bi2212 using scanning tunneling microscopy (STM). From the corresponding
Bogoliubov-de Gennes equation we find that with increasing temperature the
magnitude of the bound state energy increases and the amplitude of the fourfold
contribution in the spinor wave functions decreases. In the pseudogap regime
above T_c the fourfold angular dependence of the local tunneling conductance
persists as long as the superconducting fluctuations are sufficiently strong to
support a finite local order parameter. Once the gap function vanishes
completely, the angular structure of the bound state wave function becomes
featureless. These effects should be observable in STM studies of impurity
doped high-temperature superconductors.
