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Heat and Light do not have mass. They do not even occupy space.
That is because, something that have mass have weight, and heat and light do not have weight, they just have their temperatures, and colors. Light is made up of photon, a photon is a weightless material.
And a matter, do have mass and occupies space. A matter is either solid, liquid, gas, or plasma. You cannot identify what kind or type of matter heat and light is, so therefore heat and light do not occupy space.
Something that occupies space, and have its mass is a matter. And something that cannot occupy space is when the space we think is occupied by that something is occupied by another something, imagine light from the sun, it somewhat like occupies a space in our eyes, but when we put our hands in light of the sunray, we noticed that we occupied that space we think they occupies.
And that is the main reason why heat and light DO NOT have mass and DO NOT occupies space. 
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heat and light do occupy space.
No, they do not. :)
Matter are things which occupies space, matter is either a gas, liquid, or solid. Do you know of which of these states of matter does heat and light belong? :-)