ktypelinear.h

// corrected temperature reading for a K-type thermocouple
// allowing accurate readings over an extended range
// http://forums.adafruit.com/viewtopic.php?f=19&t=32086&p=372992#p372992
// assuming global: Adafruit_MAX31855 thermocouple(CLK, CS, DO);
float correctedCelsius(float thermocoupleVoltage,float coldJunctionTemperature){
   
   // MAX31855 thermocouple voltage reading in mV
   // float thermocoupleVoltage = (thermocouple.readCelsius() - thermocouple.readInternal()) * 0.041276;
   
   // MAX31855 cold junction voltage reading in mV
   // float coldJunctionTemperature = thermocouple.readInternal();

   float coldJunctionVoltage = -0.176004136860E-01 +
      0.389212049750E-01  * coldJunctionTemperature +
      0.185587700320E-04  * pow(coldJunctionTemperature, 2.0) +
      -0.994575928740E-07 * pow(coldJunctionTemperature, 3.0) +
      0.318409457190E-09  * pow(coldJunctionTemperature, 4.0) +
      -0.560728448890E-12 * pow(coldJunctionTemperature, 5.0) +
      0.560750590590E-15  * pow(coldJunctionTemperature, 6.0) +
      -0.320207200030E-18 * pow(coldJunctionTemperature, 7.0) +
      0.971511471520E-22  * pow(coldJunctionTemperature, 8.0) +
      -0.121047212750E-25 * pow(coldJunctionTemperature, 9.0) +
      0.118597600000E+00  * exp(-0.118343200000E-03 * 
                           pow((coldJunctionTemperature-0.126968600000E+03), 2.0) 
                        );
                        
                        
   // cold junction voltage + thermocouple voltage         
   float voltageSum = thermocoupleVoltage + coldJunctionVoltage;
   
   // calculate corrected temperature reading based on coefficients for 3 different ranges   
   float b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10;
   if(thermocoupleVoltage < 0){
      b0 = 0.0000000E+00;
      b1 = 2.5173462E+01;
      b2 = -1.1662878E+00;
      b3 = -1.0833638E+00;
      b4 = -8.9773540E-01;
      b5 = -3.7342377E-01;
      b6 = -8.6632643E-02;
      b7 = -1.0450598E-02;
      b8 = -5.1920577E-04;
      b9 = 0.0000000E+00;
   }
   
   else if(thermocoupleVoltage < 20.644){
      b0 = 0.000000E+00;
      b1 = 2.508355E+01;
      b2 = 7.860106E-02;
      b3 = -2.503131E-01;
      b4 = 8.315270E-02;
      b5 = -1.228034E-02;
      b6 = 9.804036E-04;
      b7 = -4.413030E-05;
      b8 = 1.057734E-06;
      b9 = -1.052755E-08;
   }
   
   else if(thermocoupleVoltage < 54.886){
      b0 = -1.318058E+02;
      b1 = 4.830222E+01;
      b2 = -1.646031E+00;
      b3 = 5.464731E-02;
      b4 = -9.650715E-04;
      b5 = 8.802193E-06;
      b6 = -3.110810E-08;
      b7 = 0.000000E+00;
      b8 = 0.000000E+00;
      b9 = 0.000000E+00;
   }
   
   else {
      // TODO: handle error - out of range
      return 0;
   }
   
   return b0 + 
      b1 * voltageSum +
      b2 * pow(voltageSum, 2.0) +
      b3 * pow(voltageSum, 3.0) +
      b4 * pow(voltageSum, 4.0) +
      b5 * pow(voltageSum, 5.0) +
      b6 * pow(voltageSum, 6.0) +
      b7 * pow(voltageSum, 7.0) +
      b8 * pow(voltageSum, 8.0) +
      b9 * pow(voltageSum, 9.0);
}

// (uncorrected max31855 temp)/1.3 - 5