Lets make it simple with simple quantum mechanics. water is consists of Hydrogen and Oxygen. Oxygen have bigger nucleus so it pull electron in hydrogen but hydrogen won't let it go so Hydrogen trying to pull it in but unfortunately, Oxygen is heavier and have stronger nuclear force than hydrogen. Oxygen even able to pull 2 Hydrogen atom.
Okay, we know Oxygen is such a muscular macho savage guy with a mustache and every atoms are such a thug compton gangster but what exactly happen ?. Those make water polar. because the hydrogen electron is pulled towards oxygen. The unequal distribution of force inside hydrogen atom make it slightly positive due to the induced dipole during the bodning process. That's why we classify water as polar covalent compound. And of course oxygen have slightly negative polarity because it must maintain the stability of its own atom and bonding.
What is capsaicin ?. Capsaicin is huge hydrocarbon. based on the nucleus force analysis it is nonpolar. They have polarity but not much. they have negative polarity in C=O double bond. THey also have O-H in one of its end. And a little bit positive but in really-really tiny amount of polarity of N-H binding.
So, what will happen if I put capsaicin in the water. well, water is friendly Rey Mysterio and Capsaicin is unfriendly Big Show. Water attach to some of capsaicin polar ends and try to pull it. Unfortunately to pull one capsaicin molecule, Water need more energy because it is heavy and repulsive in much ends. But, C=O ends is seems attracted to water so, it would basically able break apart and bonding with water. C=O Double bond have negative polarity, Hydrogen in water have positive polarity so, it able to pull out Oxygen from capsaicin. Yes, without any energy given to the reaction it's can be (roughly) 95-99 % unsoluble in water.
But we know, of course, reaction sometimes requires energy. Say we need to shake it, Blend it, Boil it, Electrolysis, or even burn it. Just give it energy. The solubility able to increase. But, How far it would likely to increase ?. As you notice, in repulsion of homopolarity there's energy needed to destroy this capsaicin. It's the weakness, just put up an effort to have certain amount energy which is exert the repulsion energy between capsaicin and water.
So, what happen to you is natural. When you heating up water. The orbitals of water is changing due to the electron vibrations. There's some amount of kinetic energy absorbed and force electron to move. So, the shielding between electron in orbitals can be forced and the orbital shape is slightly changing.
That's why some of capsaicins are able to dissolved in water.
But, in your case you have coffee. Coffee is complex mixture of chemical compounds. Coffee is not only consists of caffeine it's also have a bit protein and a bit minerals. Such as potassium. So, the chemical reaction between capsaicin in coffee mixture is really complex.
But let's see why it's more dissolveable. Let's check caffeine. Caffeine is have double negative polarity C=O bond. It's enough to attract water and makes caffeine soluble in water. So, you try to dissolve capsaicin in strengthen water molecule. It's a handicap match between coffee + water againts the big show. So, who wins ? I predict the tag team win. The solubility will increase but still I predict, it will not be completely dissolve in this mixture unless you put on some milk.