When being closer and closer to a star the temperarature of your ship will increase over time and damage modules, your crew will also suffer burns and may die due to the heat or start fires inside your ship too!. Having a fire incident in your ship will also raise the temperature of the modules on fire and melt your ship's hull and armor having even more leaks.
Now you can also check the temperature inside of your ship like the image below, in this case I am too close to a star and things started to get too hot for my crew to survive.
Turning your systems off can lower the radiation leak your ship makes into space making it more difficult for enemies to find your ship or track it, but it also means that it will slowly turn colder and colder and that will affect how your crew react and survive, but if you are close to a star the temperature will raise a lot faster and be more dangerous. If you have lots of robots in your ship the temperature ratio will not affect them that fast compared to humans, lack of oxygen do not damage robots and allows easy fire management. Hull breaches decrese or increase temperature depending how close to a star is your ship, and makes your ship leak oxygen, if too much oxygen is leaked you won't be able to recycle your module's oxygen properly and some human crew members may die over time or go crazy!, but you can replenish your oxygen levels in space stations or other places.
In the following screeshot, the ship is located far from any nearby star and all systems were turned off, after some time the temperature dropped very low and started to affect your crew.
And here is when fire spreads with taking any action, some areas are getting hotter and hotter to the point that it will be very hard for your crew to get in there to extinguish the fire.
Much more to share soon.