Best approach for stable reading of Weller RT for solder station

I am making myself a soldering station, after having actually used the Weller stations that utilise the RT all in one tips i went on a search for how to use one with out having to shell out for the £1000 base station. I came across the Platino Soldering Iron on Elektor Magazines site and have set about making my own based on Arduino Mega2560 and a touch screen display because i like to be fancy.

Now my issue is getting a stable reading, i tried adapting the code from the Platino project , took a sample of the tip temp with the tip turned of 5 millis before hand, did that 10 times over and got an average, but it was still erratic at best.

So i'm starting from a clean slate and wondered in anyone had any resources they knew of to guide me towards a nice stable reading that will then allow me to make a better curve for the PWM heating of the tip so that i can keep it at a target temp and not have it swing wildly 20-30 degrees in either direction.

The temperature is almost certainly a K type thermocouple, and they give a very small output - only 40uV/C.

The soldering iron and it's wiring have lots of 240vac knocking about, so it's not surprising that minor capacitive coupling can inject noise.

Fit a low-pass filter on the thermocouple with a longish time constant. Use eg 100k resistor in each lead and a 100uF across the arduino shield input.(I presume you're using one)