Thermistors work very well in the range of temperatures you need.
Perhaps thermistors are better for your application, since with thermocouples you need amplifiers, seeing that the voltage are small.
Plus, with thermocouples you have to be more careful, since all the connections between dissimilar metals between the thermocouple and the amplifier can turn into parasitic thermocouples that affect your measurements.
Also, since thermocouples only measure the temperature difference between the "hot" and the "cold" junction, you need another circuit (the cold-junction compensator) to read the actual absolute temperature of the "cold" junction to be able to calculate the temperature of the "hot" junction (and of the meat).
So it seems that thermistors are better suited to your application, since they will give you higher voltages, which you can convert directly. Since the output voltages are higher, you do not really need to care about the parasitic thermocouple effects. And since the currents are low, the voltage drops across the connecting wires are generally not a problem.
As for the hardware, you can configure the A/D for single-ended operation, giving you 8 channels.
Nonlinearity is present even with thermocouples anyway, even though it is not as bad. But the non-linearity and even calibration (for better accuracy) can be taken care of in software. This can be done for every sensor separately. Usually, a calibration at 2 points is sufficient. The rest will be interpolated, following the table from the manufacturer's datasheet, with the values scaled accordingly by the constant(s) you calculate of-line during the calibration.