Sory for my ignorance but i thought stealth mode and silent running were one and the same thing, there is a mode other than silent running that decreases your heat signature?
Stealth mode covers a couple of different styles.
Silent running ensures you don't emit heat, but it also increases internal temperature quickly which is risky. You want to turn off all non-essential power usage of course to reduce this.
The alternative is, with a good power plant, strip your systems down so that when running at full power you are at as low as possible use. Then, when about to dock, turn off everything you can. Life support, shields, etc. Well, turn off everything except life support and wait until you cool, then turn it off. Then boost towards the station and turn off thrusters with flight assist off. If you get it 100% right, you will glide right in without detection. More likely, you will need a course correction, so turn on thrusters as you are close and make those adjustments.
Its riskier than using silent running due to the trickiness of docking, and generally speaking, your heat signature is going to be higher, therefore increasing the chance of detection. But it is a viable alternative and you don't have to worry about overheating.