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Second order perturbative corrections to electron wavefunction are calculatedhere at generalized temperature, for the first time. This calculation isimportant to prove the renormalizeability of QED through order by ordercancellation of singularities at higher order. This renormalized wavefunctioncould be used to calculate the particle processes in the extremely hot systemssuch as the very early universe and the stellar cores. We have to re-write thesecond order thermal correction to electron mass in a convenient way to be ableto calculate the wavefunction renormalization constant. A procedure forintegrations of hot loop momenta before the cold loop momenta integration ismaintained throughout to be able to remove hot singularities in an appropriateway. Our results, not only includes the intermediate temperatures T m (where mis the electron mass), the limits of high temperature T>>m and low temperatureT<<m are also retrievable. A comparison is also done with the existing results.

Second Order Thermal Corrections to Electron Wavefunction