  Magnetic moment of electron at finite temperature is directly related to the
modified electron mass in the background heat bath. Magnetic moment of electron
gets modified when it couples with the magnetic field at finite temperature
through its temperature dependent physical mass. We show that the magnetic
moment of electron becomes a complicated function of temperature and even
change its temperature dependent behavior around the energies for primordial
nucleosynthesis. We calculate the self-mass induced thermal contributions to
the magnetic moment of electron, up to the two loop level, for temperatures
valid around the era of primordial nucleosynthesis. A comparison of thermal
behavior of the magnetic moment is also quantitatively studied in detail,
around the temperatures below and above nucleosynthesis temperature range.
