Hi Raghunathan,
In relation to your project, I will give some information about my past experience.
When controlling the temperature above room temperature, then you have to use a heater.
When you want to control the temperature way below room temperature, then you have to use a compressor. And when you want to control the temperature around room temperature +/- 10 Deg. then you need to use a heater and a compressor as Erik had mentioned.

Well, Here is the major difference when you control the temperature with a heater and a compressor. You can turn ON or OFF the heater at any time (mainly decided by PID loops). You can turn ON and OFF even in milliseconds.
But with the compressors you CANNOT do so. The compressor can be turned OFF anytime, But before you turn it ON again you have to give a 3 minutes delay before you turn the compressor ON. So at power ON almost every machine using compressor, gives a 3 minutes delay. This 3 minutes delay is required to increase the life of the compressor. (I do not know how, but this is the statement I got from the manufacturers of the compressor).
This 3 minute delay will seriously hamper your control algorithm.
I hope you have thought about this matter.
With the heaters (where you can have fast switching On and OFF of the heaters), you can use SSR which will give better performance than the relay(contactor) based system. But for cooling applications there is TECHNICALLY no big advantage in changing from Relay Based system to SSR based system. There maybe other good reasons for shifting over.

The above information is based on my past experience about 4-5 years back. I don't know if there has been any technical development in solving the 3 minute delay problem in compressors. I am totally out of that field now.

Thanks, and best of luck.
With best regards from,

Mr. Kiran V. Sutar.