The mistake in your question is imagining that “light energy”, “radiation” and “heat” are different things in this question. The heat in question is infra-red radiation. The light energy is the same thing as visible light, which is also a type of radiation.
These are all the same thing, which is photons that are produced by the sun’s reactions, fly through space, enter the atmosphere, and smash into the plant, transferring some energy to it. The energy is used for chemical reactions.
The only difference between “light energy”, “heat” and other types of radiation is some properties of the photons that aren’t important for how the process works. The plant is better at absorbing some types of photons more than others and the sun emits more of some types of photons than others but that doesn’t really matter for the question.
This whole topic is called “electromagnetic radiation” if you want to learn more about it, and it covers visible light, infrared heat, radio waves, x-rays and microwaves.
NB. Saying that the radiation is “photons flying through space” is a simplification that I think is appropriate for ELI5. There are other ways to think about what is moving from the sun to the plant, but it’s enough for this question to say that the sun’s reactions produces some kind of products that travel to the plant and impart energy to it.
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