I posted some stuff about silent running
here; look through that for an explanation of things I take for granted in this post.
Silent running eliminates the heat-component of your EM signature, which is what gets you detected. All ships have a sort of "base EM signature" no matter what you do. Cold running (switching off modules) reduces that signature further, but obviously, you can't use what you switch off. By using cold running + silent running, you can reasonably boost without huge risk, but you will still heat up a lot. Good luck using cold running in the heat of battle, but if you can, bully for you
I don't actually know if firing weapons/using booster when silent running actually affects your EM profile though. Yes it'll generate more heat, but the heat effect on EM is nullified due to silent running. Presumably "shoving a huge bunch of energy to a weapons/engine system" would light your EM profile up though, albeit only briefly.
Honestly, I don't know though. I know EM signature is what makes you "detectable" on sensors, and that your actual EM signature isn't visible in game, only your heat generation.