Hi,
You can not switch thermocouple leads with a multiplexor. The interface chips are not expensive; you then activate one thermocouple/interface at a time using their Chip Select lines..
See these pages:
http://arduino-info.wikispaces.com/Brick-Temperature-Thermocouple
http://arduino-info.wikispaces.com/Project-GlassKilnController-Code
You can search on 'thermocouple" and see how multiple thermocouples are handled. This works well for me and is stable on a high-temperature kiln.