With no cold junction compensation you should not get more than ~10C error according to that AD-369 datasheet, but that is including ambient temperatures well outside of human comfort.
NIST publishes tables/formulas for calculating temperature from thermocouples if you use a plain A/D converter. An MCP3424 would give you four channels for ~$4 and you can have up to nine on an I2C bus. But it's a SOIC and the 18bit conversion rate is a bit slow (3/second).