Actually for this question you need to get into the derivation part ..
Let us consider the Electric field be E and is acting on an electron having charge q.
Then due to force the electron will start moving from its rest position and will get collide to the other electron..this time taken in one collision is a constant value which depends on object's temperature...If temperature is high then electron will have more K.E and then they will move fast and thus collision time will decrease and vice-versa
Then Force on the charge will be qE.
Acceleration = qE/m
Initial velocity = 0
Final velocity = v
Then v = 0 + (qE/m)t
or V = qEt/m
Avg velocity (Drift velocity) = qEt/2m
Where is the collison time...and depends on temperature...