The project is to make a constant temperature cabinet. A good commercial example is the Memmert ISP260.
I propose to use Arduino, an old PC power supply, and two heat sink/fan assemblies that sandwich a Peltier cooler.
How can I use the arduino to switch polarity on the Peltier so one device can be used to provide heat or cooling as required?
I'm an old programmer and just aquired electronics for this project. I believe I have the programming nailed but how and what to use with the ardrino to switch polarity on the Peltier has me currently stumped.
Hope someone can shine a light.

 

use a DPDT relay, 5 v coil or 12v coil, drive the relay with a transistor.

the motor is your Peltier device

http://www.yenka.com/activities/Double_Pole_Relays_-_Activity/

 

Hope someone can shine a light.

There's your answer. Use a lightbulb as a heat source and design the peltier to only cool. Much simpler.

 

If you wanted to do it with all electronics you could use a MOSFET bridge circuit, but a relay is simpler and has a lower voltage drop.

 

Don't forget to include an "off" position, where it is neither heating nor cooling.

 

Use an H-bridge.