I reckon you need a new button, but your chime might be faulty as well.
If the button is heating up, it means 2 things are happening:
- There's current flowing through it, and
- It's got a noticeable resistance.
There shouldn't be current flowing through it when it's not being pressed, so either - it's sticking, or
- you have a chime that manages to draw current when the button is released, and that's sticking (some do, some don't and we don't know what you have*).
Corrosion inside the switch can cause both mechanical sticking and electrical resistance, which is why it would be my first guess. But the fact it's showing a resistance means even if there's another fault, the button still isn't right. This is true to some extent for illuminated buttons as well, except that if they are illuminated with an incandescent bulb, that will get quite warm. LEDs and neon bulbs (orange) won't.
* I don't know about what's available wherever you are, but here we have 3 main types of chime:
- electronic, which can clearly draw current after the button is released, as they keep sounding. Can make any sound.
- two metal chime bars. A solenoid pulls a striker towards one when the button is pressed, and a spring bounces it off the other when the button is released. No chance of current draw if the switch opens properly. "Bing-bong" sound.
- An electric bell with a clapper, sounds a little like a telephone bell. Here the clapper is pulled towards the bell by a solenoid when the button is pressed. The same action causes the circuit to be opened, so the clapper springs away from the bell, but then the circuit is remade, causing another strike for a brrrrrrring effect. Again, no current should be drawn without the button pressed