I don't know what is causing the problem, ADC is not always as straight forward as it should be.
I can suggest a few pointers
1) verify that there really is cross talk between the two channels by using two potentiometers (or 4 resistors) with a total impedance of less then 10k. If the ADC is okay then the output impedance of the MCP9700 is too high, although according to the data sheet is only 20R
2) If there is still a problem when using the pots. then look at the sampling rate and acquisition time, slow these right down or speed up see the effects.
3) Filter the output of the MCP9700 using a capacitor, say 10uF, assuming that temperature does not change that fast.
Hope that helps