Would in theory be possible to have a similar reaction that burns something without releasing heat?
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There are plenty of chemical reactions which remove heat rather than releasing it, they are called endothermic reactions. But the way combustion is defined limits it to specific kinds of reactions that release heat (called exothermic reactions).
It takes energy to break the chemical bonds between atoms in a molecule. Energy is also released when atoms come together to form bonds. If the energy that goes into a reaction is less than the energy that comes out, that makes it exothermic. Combustion is exothermic for this reason. The heat you put into it (to start the fire) is less than the heat that comes out as a result of the formation of new bonds between atoms as a result of the reaction.
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