So when you feel the sun’s warmth, you’re not feeling heat coming from the sun. You’re instead feeling heat created *on your skin* by the sun’s light.
Light carries energy. Things with colour, like your skin, absorb light. When they do, the atoms that make them up get ‘excited’. Depending on the atom, and what state its in, a few things can happen. If the atom is part of a molecule that energy can go to work breaking it out of the molecule. If the atom or molecule is on the surface of a solid or liquid, the energy can go towards flinging it off, into the air, turning into a gas.
If there’s not enough energy to do either of those things, then the atom will just release the energy to its surroundings. Most of the time, most of the energy is released as heat. This is what you feel when the sun feels warm. Sometimes the energy can be released as light. This is how glow-in-the-dark things work.
A cloud doesn’t block all the light from the sun, but it does ~~absorb~~ *scatter* a lot of it. *Think of water droplets in a cloud like a million tiny disco balls*. The light that gets through is either too sparce to be noticeable, or high-enough energy that it causes damage instead (ie. UV light).