Hi Max,
There are many things unknown to me with respect to your system. I'm not sure how you are calculating your temperature, the accuracy/# wires of the RTD, the currents used for excitation, etc.. The problem is you cannot just convert the calculated resistance to temperature with a simple equation as the RTD is not a totally linear device.
For a two point calibration you are basically trying to discover the slope of the transfer function as it differs from the ideal. This slope is independent of the offset, but relates directly to gain. It is best to deal with both offset and gain. The easiest way to deal with offset is to issue a SELFOCAL which places an internal short on the input mux and OFC register contents are adjusted so as to output a 0 code for the shorted input case. This does not account for any offset error caused by external sources, but it will cover the ADC itself and automatically adjusts the result accordingly. This command can be issued at any time and should be done before any other calibration.
As for the problem you are seeing with the ADS1147 output, you should not see much effect from the ADC itself if the temperature environment of the ADC is relatively stable. Have you plotted your results so I can see them? If you are using a temperature chamber, it is difficult to get good repeatability as the air currents in a chamber may not allow for an even temperature. Usually a bath is a much better approach, especially for calibration.
How are you calculating the temperature? Are you using lookup tables? Direct calculation? How much deviation from the expected values are you seeing? Are you accounting for the non-linearities of the RTD?
Best regards,
Bob B