Hello Commanders!
Just thought maybe i could help out with explaining "rigged for silent running".
Ship heat: As you power draw increases (from turning on modules that require power), your power plant generates heat inside the ship. This is represented by the heat bar to the left of your sensor disc.
The effects of heating up your ship are that eventually some systems might shut down and the ship will start taking damage - effectively cooking itself.
Separately from this, your ship has a signature, which describes how visible you are to other ship's sensors. As heat is radiated out, your signature increases. This radiation rate is not the same as your internal ship heat, though obviously there is a direct connection. The hotter your ship is, the more heat it's radiators put out, and the bigger its signature.
When you rig for silent running, you close off your ship's radiators. Your ship still generates heat and cooks, but to other vessels it appears cold. As part of silent running you also turn off shields as the context is that these effectively radiate heat directly.
So how does signature work? Well, the smaller your signature, the closer a ship has to be before its sensors will detect you as a fuzzy contact (where the sensor marker flickers and moves around) and then as a resolved contact.
You can gain a similar benefit that silent running gives you by manually turning off modules. Your power plant runs cooler so less heat is generated and radiated. However, unless you basically turn off everything (including life support) the effect will be less effective.
There are two caveats to silent running benefits:
A) when your ship gets very close to another vessel its sensors will be able to detect you even if you are rigged for silent running. This auto-resolve distance is normally around two to three hundred metres.
B) ships can be fitted with more powerful sensors that increase the distance that they can detect you, and that can push the auto-resolve distance out to around five hundred metres or more (good sensors are the silent runner's worst nightmare).
All this being said, silent running can be used during combat, but it's a very dangerous gambit. Missiles, turrets and gimbal-mounted weapons *do* use signature to determine when they can lock on, so going silent can often make them lose lock until you are very close. In fact, if you rig for silent running and you're not within auto resolve distance then an aggressor will not even be able to target you to check your shield/hull status.
Silent running is certainly most effective at range, of course, out beyond the auto-resolve distance.
It's also important to note that we specifically did not want a "cloak" stealth ability that was indefinite, which is why silent running has various limitations.
Hope this helps a bit.