HI,
I have one peltier connected to fan and heatsink and power supply.
I have doubt, when i disconnect power supply and peltier then peltier is showing short between two wires(fan were connected to peltier).
I don't know much about peltier principle.
But i have doubt whether it is working or not. Because fan and peltier were connected together and when i checked continuity then it was showing short.

 

A working module will show a resistance below 2 ohms, possibly below 1 ohm with a fan in parallel. Depending on your ohmmeter, this low resistance might appear to be nearly a short.

It’s easy to test the fan separately to make sure it’s spinning when voltage is applied. With the peltier you can briefly apply power and see if one side gets cold as the opposite side gets hot. Don’t let this go too long, the module can overheat and damage itself.