Hi,
What is the maximum amount of energy that can be stored in
1 gram of matter (take your choice of matter) ?

Well, Mr Einstein says the answer is 90e9 kJ (E=mc^2), and matter doesn't matter ;)

I do not want to convert the matter to energy , but suppose I heat the mass upto x degrees so the mass will store some amount of energy , is their a theoritical limit of how much energy a mass can store ?

As Ancient Dragon asked, what is the point of the question?
Maybe it should be asked at a scientific forum? :)

Me thinks emilo35 answered your question with a quote from the master.Later---

I do not want to convert the matter to energy , but suppose I heat the mass upto x degrees so the mass will store some amount of energy , is their a theoritical limit of how much energy a mass can store ?

Yes because temperature is actually a measure of the motion of the molecules/atoms making up the matter and the fastest anything can move is the speed of light so the upper limit on the temperature you can raise the matter would be equivalent to the speed of light -> however nothing with mass can reach the speed of light so you could never actually heat something up to that temperature.