Solution
In short words, using regular analog input (AI) modules is not recommended for taking thermocouple measurements.
The resolution and voltage range for most of the AI modules are not suitable for thermocouple measurements. For example, the NI-9201 has fixed voltage range of +-10 V and a resolution of 12 bits. This means that the maximum resolution achievable is of 20/2^12 = 4.88 mV. Thermocouples vary in the order of uV/°C given by the Seebeck coefficient (i.e. 56uV/°C for a J-type).
Using temperature modules such as the NI-9210, NI-9211, NI-9212, NI-9213 and NI-9214 will give much better thermocouple measurements. You can also find temperature modules in the PXIe form factor such as the PXIe-4353.