How to determine the value of a decoupling capacitor across a Peltier device?
To determine the  value of the decoupling capacitor between the TEC you will have to see the effect of the thermal noise on the switching done by the OSC in your driver usually a PWM.

The TEC works on the reverse SEEBECK effect,the change in the temperature on the two surface,causes the current to flow,this condition is reversed by using a driver where the current flow is modified,

The Usual ICs Design will Use Some pins to sense the Output(V) at the TEC terminals,
and a resistor placed to act as a V-I converter often called Current sense.
Please Notice there are lot of variants in the market each with different design here I will prefer only DC based ICs so if yours is a bit different please bear with me.

The TEC current values are controlled and switched by sensing these Output (Often called Ouput sense).

To make the system more regulatory the switching can be made in two mode,(one faster and the other slower (there are still some IC using one switching frequency,and yet some providing upgrade based on your designed ckt ).

Mostly Companies use PWM  based switching,these frequency switches of TEC uses OPAMP Oscillators.
Typically they have a band of &lt;-20deg C to &gt;80deg C,hence there are lot of thermal and thus current variation to account for,

Often the Switching to be done is influenced by the Thermal variation these switching are basically done with a help of Oscillator,hence  to cancel thermal noise Capacitors are used.
When generating cold, the TEC moves the heat away from its cold side to ts hot side as the current flows into the positive terminal. The higher the current, the larger the amount of the heat is moved. During this process, heat is generated on both sides. When the current is increased to a certain level, the heat generated by the current on the cold side equals the heat being moved away from the cold side, the temperature on the cold side stops dropping, i.e. the TEC’s thermal output power becomes zero.  

Most Ics has max 6-8A current limit.