I personally have no experience of calibrating this unit so will be baseing my answer on the NI resources I have available.
The one year calibration is recommended by NI to maintain the systems optimum accuracy. This time frame can be adjusted depending on the accuracy requirements of your testing procedure. Within the Calibration Procedure manual for the NI 4353 details of the expected test limits after one year can be found on pages 19-22 for different temperature ranges and thermocouple types.
The Ectron 1140A has been selected as the recommended calibration system for the device. However a high precision voltage source with an accuracy of at least 70 ppm and an output impedance of ≤10 Ω can be used for voltage accuracy verification and a thermocouple calibrator with an accuracy of 0.10degC when sourcing 100.00degC with a K type thermocouple. Details of this can be found on page 3 of the calibration manual.
I hope this information helps you, and if you need any further advice please feel free to get in touch.