Your diagram:
Why do you put the two CLK and DO on separate Arduino pins? They should both be on the same pin. i.e.
Pin xx = CLK1 and CLK2
Pin YY = DO1 and DO2
Pin ww = CS1
Pin ZZ = CS2
Unless you have a specific reason for not, you should use the Normal SPI pins (see any board pinout).
From an earlier post I understand this is your board:
What Arduino are you using? if you stated it above I couldn't find it.
There are only two Max31855 boards I am aware of:
- your board
- A MAX31855 board with 5 -> 3.3 Volt regulator. Although they may exit I've not seen one with signal level converter circuitry.
- The Adafruit board (which is also a general eBay board)
The 2nd board is superior only because it has additional components to help filter the noise off a thermocouple signal with is very small.

Wait, so you think the Adafruit Board is superior or the Maxim one
They are all Maxim boards because they all use the Max31855 integrated circuit.
