Cockroaches survived the extinction that killed the dinosaurs. They were the rulers of the Carboniferous period which took place one hundred and twelve million years before the dinosaurs and three hundred and sixty million years before us. They are highly adaptive, resistant to all forms of radiation from photonic solar radiation to particle radiation like gamma, beta and alpha radiation. Cockroaches can withstand deadly heat that would kill a mammal but unlike mammals, they do not have their own heat source. This means there is only one thing that can kill them, the cold. But then how did they survive the ice age. With the help of humans of course.
The ice age was very recent, only ten thousand years ago really and humanity was very much around alive and well. They had already discovered how to use stone and bone as a tool and some cultures even learn to wield metal like copper, bronze and even iron. These people had homes either built or in caves that were hewn to suit their needs. The cockroaches being so small and easy to miss would take advantage of our hearth and take in the heat when it was too cold. Without humans, the cockroaches would not have survived the ice age.
This same situation happens today as winter approaches cockroaches tend to rush into homes. They do not prefer to live outside but are willing to when it is hot. Though with a drop to just ten degrees celsius the cockroaches can suddenly start dying from the solidification of their internal organs. They have no internal heat production to stave this off and will die even in a light winter.
This is not how you kill them however, turning the heat off in your home will only annoy you. They can handle down to ten degrees and that is more than you will be able to handle trying to sleep in your freezing cold house. They, of course, are tiny and will be able to find warms in cracks and crevices. So if you have cockroaches the last thing you should try to do is open the door. That would just let more of them in.
If you have cockroaches you can get rid of them on your own with a series of domestic treatments. Over time they will reduce and stop. However, this can only be done with a new infestation and will do nothing for any sort of commercial building like a library or a restaurant. Anywhere people can bring food or that has food stored can attract them and it is very difficult to remove them from a place where the public are allowed in at a whim and the door keeps opening and closing. Be glad the infestation is in your home and not your office.