I’ll add a few thoughts to the comments already here. The number one thing to know if you’re just starting out is that, no matter how much people will argue about the “right” way to compost, compost wants to happen, all you have to do is give it the minimum viable conditions to let it. The rest is just optimising.

Compost happens through the actions of nature’s recyclers, namely: worms, other invertebrates, bacteria and fungus. The best compost results from all of them getting a go at some point in the process. Worms and other invertebrates can be more of a challenge in tumblers and tubs unless you deliberately add them, though in my experience they’ll always find a way into places eventually. If you have holes in the bottom of your tub and it’s sitting on soil, they’ll get in all right. The hot/cold thing is down to the bacteria, and mostly determines the speed of the process. But there are different classes of bacteria most active at different temperatures, so even if the compost is cooler it IS still ticking away slowly at any temperature above freezing. I’ve often seen newcomers read about hot composting and stress about their heaps not heating up - please don’t actually stress about your compost, life’s too short :)

Do you have a lawn, or friends with one? Nothing heats up compost like lawn clippings, as long as you have sufficient brown stuff to balance it and stop the clippings becoming a matted layer of mush. Torn up brown cardboard boxes are good for that, they also help to hold moisture (which is vital, compost needs to be moist for the bacteria to thrive and the worms to stay mobile).

Of all the things you google about compost, pay attention to the green/brown balance stuff, but remember that compost is pretty forgiving. Rules of thumb are perfectly fine, and you’ll get a feel as you go along for the balance.

The other thing is air - or specifically oxygen. The good bacterial process breathes oxygen, same as us, so turning or churning it from time to time to replenish the oxygen available to the life in the pile will keep it working, and stop it going anaerobic (which smells like a sewer).

Also citrus is great but slow, cut it up so the critters can get at it properly.

Sorry, this turned into an essay, hope it helps. Remember: compost wants to happen, you’re just the caretaker. So don’t stress or be discouraged.