TomGeorge:
Hi,
Welcome to the forum.
Please read the post at the start of any forum , entitled "How to use this Forum".
OR
http://forum.arduino.cc/index.php/topic,148850.0.html.
What are the specs of your Peltier Device(s)?
How many are you using?
How are they wired?
Do you have temperature sensors on BOTH of the Peltier faces?
Thanks.. Tom.. 
Thank you. I am using peltier element TEC1-12710. Specs of the Peltier are;
Umax = 16V / 17.2V
Imax = 10.1A
Temperature Difference between cold and hot side = 70C/79C
Cooling Capacity = 101.1W/110.5W
I am using 4 of these Peltier elements. They are placed on a Brass Profile Pipe along with thermal mass on each of them(heatsinks and fans). Two of the peltiers are placed on the upper side of the pipe and the other two are placed on below of the pipe.
They are currently not wired. I am open to suggestions on this and every part of the project. I am running tests on a separate TEC1-12710 model Peltier.
I don't have temperature sensors on either side of the Peltier. One is obscured by heatsink and fans and the other is directly connected to the brass pipe. I plan on placing sensors on In and Out of brass pipe, calculation temperature of the water entering and leaving, and on the brass surface of heat exchanger.
gilshultz:
I like your choice of the BTS7960B, I use them a lot. The module is built with 2 half bridges, and each chip surprisingly has a lower RDSon on the high side FET then the low side FET. The resistance of a relay is much higher then this device especially after the relay is used for a while. You can use this as a High or Low side switch or bridge. If you change your mind about PWM it will do it just fine. I ran ten amps through one the other day without a heat sink and it did not get noticeably warm. They are good modules.
Thank you. Drivers should arrive by cargo tomorrow. I want to test them out.
Using Peltiers with PWM is getting more confusing more I read about it. They say it is not usually used because nothing heats-up or cools down as fast as the PWM signal. Some say it is only an academic problem. Others say just put an inductor in series to PWM and it would be alright. I am quite confused.
jimLee:
A PWM is on/off lots of times a second. Just turn it on and don't turn it off 'till you're finished with the heating/cooling cycle. You can do this with a couple relays, you don't need anything fancy. I mean your just basically doing the same thing as turning on a light bulb. That draws a bunch of power.
-jim lee
I think I understand. The heater should start when the temperature is below the target and turn down when it is slightly above the target temperature. Same for Cooling. My only concern is stressing the Peltier too much by making high-temperature changes on the same side of Peltier.