What is the mechanism by which the ortho- and para- spin isomers of hydrogen interconvert?
If such a mechanism exists, does this mean that ortho-hydrogen increases in concentration on increasing temperature?
The first question is:
What is the mechanism by which spin isomers of hydrogen switch between the ortho and para forms?
One can define three situations. In the first, a magnetic conversion occurs without bond elongation or breaking. For example, in solid dihydrogen dipolar magnetic nuclear interactions are responsible for an extremely slow spin conversion. In the presence of unpaired electrons the conversion is accelerated by the magnetic hyperfine interaction. The second situation also involves a magnetic conversion mechanism, but is assisted by an intermediate H–H bond elongation, for example, by binding to a transition metal center. Finally, in the third situation, a H–H bond splitting and re-formation with other hydrogen atoms occurs, which corresponds to a chemical spin conversion.
The second question is:
If such a mechanism exists, why does ortho-hydrogen not increase in concentration on increasing temperature?
The equilibrium fraction of ortho-hydrogen does increase from 0% at absolute zero to 75% at high temperature.
para-Hydrogen is the lowest energy, most stable form, since it is capable of accessing the $J=0$ rotational level (whereas ortho-hydrogen cannot). There are three microstates corresponding to ortho-hydrogen:
$$|\!\uparrow\uparrow\rangle, |\!\downarrow\downarrow\rangle, |\!\uparrow\downarrow\rangle + |\!\downarrow\uparrow\rangle,$$
but only one microstate for para-hydrogen:
$$|\!\uparrow\downarrow\rangle - |\!\downarrow\uparrow\rangle.$$
So, according to the Boltzmann distribution, the equilibrium fraction of ortho-hydrogen goes from 0% at 0 K to 75% at infinite temperature (in practice, a temperature at which the effects of rotational quantisation are not seen).