Powering thermoelectric cooler and fans with 12V input
The fans can be connected directly to the 12v supply. This leaves 4.12-0.2-0.2= 3.72A for the cooler. So, to ensure the PSU isn't overloaded, the TEC + resistor needs to be no more than:

Resistance = Volts/ Current
= 12 / 3.72 = 3.23 ohms

The cooler has a resistance of around 12*12/60 =  2.4 ohms. So the resistor needed in series with the TEC must be at least 3.23-2.4 = 0.83 ohms.

The minimum power rating for the resistor needs to be considered as well:

Say you choose a 1 ohm resistor. The total resistance of TEC + resistor = 1 + 2.4 = 3.4 ohms. 

Therefore the current flowing through both is:

Current = voltage / resistance
= 12 / 3.4 = 3.53 amps

So the minimum power the resistor must ba able to handle:
Power = Current^2 / resistance
= 3.53 x 3.53 / 1
= 12.5 watts

So in other words, you will need a particularly beefy 1 ohm resistor.