Pure breeds will lay less than crosses or hybrids. Light is the reason why they stop, not temperature per se. Although it probably has an influence too.
I find that in their first winter they lay steadily through without any additional light, but then for their second and any later ones, light to extend the day for them helps. I don't change their food other than to give mixed corn (incl maize) in the afternoons in winter, and just wheat (and less of it) during the summer. Mine have layed through minus 20 this winter, and are in their third winter! The pullets started to lay on Dec 22nd....
Most of mine are crosses by now, initially we had pure RIRs and Lt Ssxs (utility strain), but Maran cockerels and now Lt SSx have changed that...