I'm no thermocouple expert, but to the best of my knowledge you should be using a type K. This is what most gauges are calibrated to use. Probe info from wiki....
Type K -- Chromel (Nickel-Chromium Alloy) / Alumel (Nickel-Aluminium Alloy)
This is the most commonly used general purpose thermocouple. It is inexpensive and, owing to its popularity, available in a wide variety of probes. They are available in the −200 °C to +1200 °C range. The type K was specified at a time when metallurgy was less advanced than it is today and, consequently, characteristics vary considerably between examples. Another potential problem arises in some situations since one of the constituent metals is magnetic (Nickel). The characteristic of the thermocouple undergoes a step change when a magnetic material reaches its Curie point. This occurs for this thermocouple at 354°C. Sensitivity is approximately 41 µV/°C.
Type J -- Iron / Constantan
Limited range (−40 to +750 °C) makes type J less popular than type K. The main application is with old equipment that cannot accept modern thermocouples. J types cannot be used above 760 °C as an abrupt magnetic transformation causes permanent decalibration. The magnetic properties also prevent use in some applications. Type J's have a sensitivity of ~52 µV/°C.
