2N3904 Darlington Pair
1) You are trying to drive a speaker and also feed DC through the 2nd transistor - it's no-surprise the 2nd transistor gets warm - it sees a dc load that is a few ohms (the speaker) and will get hot.

2) The dc current through the 2nd transistor also passes through the speaker and this could damage the speaker. Speakers expect an ac current (as from a normal amplifier). The dc current will offset the position of the cone/diaphram and likely damage it. Sound quality and loudness will also be significantly impaired.

3) Your input signal will not take the biasing voltage you have tried to apply. The voltage source in the diagram will shunt the attempt at applied dc bias to ground - in effect, any sounds produced will be from the upper positive peaks of the signal applied.

Solutions to (1)&amp;(2) you would do better with a push-pull amplifier set-up with a capacitor feeding the speaker from the emitters of a standard pair of NPN and PNP transistors OR use an LM386 chip. I wouldn't bother trying to solve (3) because solutions to (1)&amp;(2) negate solving it BUT putting a capacitor in series with the voltage generator will allow you to see what I mean in the simulator.