Everyone knows that if you crack a core asteroid and then pilot the ship into the debris, your ship temperature drops until the screen ices up. I've seen it mentioned in videos that it is because the core, or the result of the blast, makes that area of space very cold. That's wrong. That area of space is no colder than any of the rest of the environment.
Cold is, of course, the absence of heat. There are only three ways that heat moves: conduction, convection and radiation. In conduction a cold body and a hot body in contact with each other share their heat until they are the same temperature. In convection a hot body warms the air around it, which then rises and allows cooler air to take its place. A hot body radiates infra-red light and in doing so loses energy, which results in it cooling down.
In space there is nothing in contact with your ship, so you can't use contact to cool down, (except for heatsinks.) So you can't use conduction. There is also no air and no "up" for it to move, so you can't use convection. The only way for your ship to lose heat is to radiate it. Radiation is very inefficient for cool bodies and so this is a problem that real space ship designers battle with.
See how they do it on the ISS.
The rocks in icy rings
are cold. They contain liquid oxygen, which puts their temperature between −218.79 °C and −182.962 °C. Every rock is that temperature; there is nothing special about cores. That has no effect on your ship because vacuum is a perfect heat insulator; the temperature of the rocks around you makes no difference to your ship. It is built to work in deep space where there is even less heat coming from a sun and, anyway, with a spacecraft, the problem is always cooling down, not warming up.
Except, that is, in the dense debris field immediately following the cracking of a core. The blast vapourises stuff and throws out rocks of all sizes, large and small. You hear it impact your hull when the rock cracks. The smallest rock shown when you fly into the debris is maybe a tonne, but there must be a whole host of smaller stuff too, down to grains of sand or less, and there will be a whole lot of it. Of course it will dissipate in time, drifting away and being attracted to other nearby bodies. But not quickly; the big rocks are only drifting slowly and the smaller stuff will not be moving any faster. For a few minutes following the blast, that space is not empty. One might say that it is not a vacuum, although the vast majority of it will be solid and liquid rather than a gas.
All that solid, liquid and gaseous matter makes contact with the hull of your ship. The heat of your ship is conducted into the cold particles and your ship cools down. Rather than being a strange property of cores or the explosion that cracks them, the cooling effect is a beautifully observed simulation of common physical law.