When connecting a thermocouple to an amplifier, what are the advantages of the differential versus the single-ended configuration?
Thermocouple circuits are just loops of wire, and in industrial situations may be rather long loops of wire. In this case they are subject to what is called common-mode noise, in particular high-voltage induced AC.
The idea being any induced noise will appear essentially the same on both wires, and the differential amplifier will subtract it out.
Thus differential amplifiers provide a much cleaner signal than a single ended amplifier (with one side of the input tied to ground). The ability of the differential amplifier to filter out common-mode noise is a parameter called the CMRR (common-mode rejection ratio).
Here is a thermocouple system using a number of Linear Technology parts. The differential amplifier is the LT2057 (shaded).
The least expensive and fastest-response thermocouples have a grounded junction. If your circuit also has a common ground you can tolerate a non-zero common-mode voltage on the thermocouple when a differential amplifier is used.
An alternative, applicable if there is only one thermocouple, Is to isolate the circuit form ground and allow it to float with respect to ground.
Alternately, isolated-junction thermocouples can be used, but they are both inferior in response time(meaning poorer control) and more expensive.
Here is an example of a circuit that can be used for either type- the 1M resistor provides a path for bias currents of the differential instrumentation amplifier if an ungrounded type is connected. (Actually a seasoned designer would likely use a lower value in high temperature electrically-heated applications).