In the book of The First Three Minutes by Weinberg, at page 106-107, it is stated that

SECOND FRAME. The temperature of the universe is 30,000 million degrees Kelvin [...] The nuclear particle balance has conse- quently shifted to 38 per cent neutrons and 62 per cent protons.

[...]

THIRD FRAME. The temperature of the universe is 10,000 million degrees Kelvin. [...] The decreasing temperature has now allowed the proton-neutron balance to shift to 24 per cent neutrons and 76 per cent protons.

What is the reason for this balance shift between neutrons and protons exaclty ? and what does determine this rate of the change this shift ?