Even though bcc structure is less dense than fcc, but iron undergoes bcc to fcc transformation on heating above 910 degree celsius. why its undergoing this phase transformation from a less dense phase to a more dense phase when we are increasing the randomness by increasing the temperature?
It is the relative free energy of bcc and fcc iron which determines the temperature range over which they are stable. As you are acknowledging, the randomness or the entropy plays a role in the stability of the iron allotropes. However, it is not the only player; it is in fact the combination of entropy and enthalpy which determines the free energy of each allotrope. Free energy is related to these two players (components) according to the following equation:
G: Gibbs free energy
The temperature dependence of G for iron allotropes is such that the free energy of fcc iron falls below that of bcc iron in the temperature range of 910-1395 C (under a pressure of 1 atm) and makes it the more stable of the two in this temperature interval.