does increasing the temperature of an object increase it's mass?

Ok, so I was just thinking about einsteins famous equation E=mc^2, and I was just wondering, if I were to take, say a rock or piece of metal. If I were to weigh it, and get it's mass, I could compute how much energy it contains. However, if I were to add heat to the rock or piece of metal by putting it into a fire to just heat it up, wouldn't the amount of energy that the rock or metal contains be higher, and so wouldn't the mass be higher (since the speed of light is constant, the only thing that can increase when the energy increases is mass, right?)? Anyways, maybe I'm missing an obvious point, but I was just curious about this, so any clarification would be great.
 Recognitions: Gold Member You are absolutely correct. The measured mass would increase if you heat an object up.
 Just remember that the equation E=mc^2 only applies to objects at rest. Objects in motion use the equation $E^2=m^2c^4+p^2c^2$.

does increasing the temperature of an object increase it's mass?

 Quote by mcafej Ok, so I was just thinking about einsteins famous equation E=mc^2, and I was just wondering, if I were to take, say a rock or piece of metal. [..] if I were to add heat to the rock or piece of metal [..], wouldn't the amount of energy that the rock or metal contains be higher, and so wouldn't the mass be higher [..]? [..] any clarification would be great.
Yes that is correct; the kinetic energy of the vibrating atoms in that object adds to its mass. (I don't know if it has ever been possible to measure this effect.)

See also the conclusion of the related famous paper:
http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

and a discussion of temperature:
https://en.wikipedia.org/wiki/Thermodynamic_temperature
 Does this also mean that a steel spring would be measured heavier in a compressed state than in a non-compressed state as it has stored energy?

 Quote by JustinRyan Does this also mean that a steel spring would be measured heavier in a compressed state than in a non-compressed state as it has stored energy?
Yep!