The upper chart here shows the output voltage vs. temperature for a type K thermocouple. The curve is reasonably linear, although it clearly has significant deviations from absolute linearity. The lower chart shows the deviation from a straight-line approximation, assuming a linear output from 0°C to +1000°C for an average sensitivity of 41.28 μV/°C. In practice, linearity correction can be done by calculating the actual value or by using a lookup table which maybe a throughput issue with slower MCUs.