Heat is not as essential as light. As Zach123 said, a hen is born with all the eggs they will ever lay in their lifetime. How many eggs they lay each year depends on many factors, not just season or light. Now with each breed, quantity will change, so I am just going to talk about popular breeds like Rhode Island Reds (RR) and White Leghorns (WL). Now a good RR hen will reach a peak production of eggs around 200 a year with reasonable management. You can get more out of them with perfect management, but let's just go with 200 for argument sake. About the same is true for WLs. There are some new super production breeds that will do a lot more. I read somewhere that the world record is like 370 eggs for a WL.
Anyway, let's just go with 200 eggs a year for a hen in normal farm or backyard conditions. But this will not happen naturally either in most cases, with normal RR or WL hens. One factor is that you must feed them the correct diet and provide them with calcium supplement. This part is easy. The other thing is that they are sensitive to light change. You can solve that by running a 13 watt (60w) CFL bulb in the coop 24/7. But another thing is that hens will go broody and you need to break them from this by putting them in a pen where there is no nest. Not all hens are strong brooders and most will break easy, but some are as stubborn as mules. The point is that, if you break them from their broodiness, they will go back to laying after a period of rest. But if you don't, they can go several months with laying. And if you let them set on a clutch of eggs and hatch them out, it will be up to eight months before they will lay another egg.
Now let's talk about the years of production. From an egg production point of view, you want a hen to lay as many eggs as possible before it gets too old. The older a hen gets the more irregular her laying will be and she begins to lay odd shape eggs. Hens will reach peak production about their third laying cycle. Take RR for example. They will start laying at about seven months old. These will be small pullet eggs. They will lay around 30 eggs and stop for a couple months. The next cycle they will lay about 40 or 50 medium eggs. Their third cycle they will lay around 60 nice large eggs. This is their peak under normal farm conditions. So a RR will reach it's peak laying potential around one and a half years old. They will stay here until about three years old and then start to slowly decline up until they are around five years old. I have had several really hens die naturally of what I call Egg Labor. You know it is about to happen when you start to see eggs so large you wonder if a turkey is jumping in the pen and laying them. At some point the hen will produce an egg so large it cannot lay it and the hen will die. Or the egg will rupture inside them and that will kill them. Most people get rid of their old hens long before this stage so they never see it.
Well, that is about all. Hope it helps.