That code makes a lot of sense, ensuring small changes between readings and preserving memory space for averaging. However i must admit the biquadratic filters are still a litt confusing to me, i never managed to get my head around understanding the frequency domain. The thing i am not sure about is what a hefty capacitor would be in this situation? I have modified my schematic to include the new filtering and i think it will certainly improve my results. I also ensured that i have a bypass capacitor right next to the supply & reference of my ADC so as to remove some of the noise from there.
You need to put the feedback cap in parallel with the feedback resistor - so R6 goes between the op-amp output and the inverting input and C7 goes in parallel with R6. You'll also need another cap across R8, the same value as the cap across R6.
'Hefty' means about 100nF - that's a good starting point. Use polyester film or polypropylene. You might need 47nF or 220nF, or something like that. (Normally capacitors around op-amp feedback loops are in the order 10pF or so, so 100nF is pretty 'hefty' by those standards).
If you find the op-amp oscillates with the feedback caps (it shouldn't do, but might) then put a 47R series resistor right at the op-amp's output.
That LT app note looks very useful, it's worth thinking about cold junction compensation if you need absolute accuracy - that's what the LTC1025 is doing in the diagram on page 2.
You should be ok with this belt and braces approach - the op-amp feedback caps help prevent the op-amp amplifying noise and RFI from the thermocouple, the RC filter attenuates noise even more to help prevent aliasing at the ADC, and the IIR filter gets rid of acquisition noise. You can even tweak the gain of the diff-amp to give you more output voltage so you use more of the ADC's range, as long as the maximum temperature you expect results in a voltage slightly less than the ADC reference voltage. This improves signal-to-noise ratio as well as measurement resolution and helps even more. That's the belt-and-braces-with-cable-tie-and-gaffer-tape approach.#
@andy - that biquad filter looks good, never made a digital implementation but have used their analogue counterparts a few times in audio applications. Looks like you need a micro with an FPU to use it, assuming those coefficients are doubles and not ints.