The 555 can have an output current of 200mA without getting too hot. Its max saturation voltage loss is 2.5V at 200mA which is a heating dissipation of 0.5W which is fine for the DIP-8 package that is rated at 1.18W at room temperature.
If the "9V" adapter is actually 10V and the load is capacitive-coupled to a 6.8 ohm resistor in series with an 8 ohm speaker then the output of the 555 swings from +5V to +7.5V and down to +2.5V. The load is (6.8 ohms + 8 ohms)= 14.8 ohms and the 2.5V peak voltage across it causes a current of only 169mA. The heating dissipation in the 555 is 2.5V x 169mA= 0.42W. It will be pretty warm but not too hot.
If the "9V" adapter is actually 10V and the load is capacitive-coupled to a 6.8 ohm resistor in series with an 8 ohm speaker then the output of the 555 swings from +5V to +7.5V and down to +2.5V. The load is (6.8 ohms + 8 ohms)= 14.8 ohms and the 2.5V peak voltage across it causes a current of only 169mA. The heating dissipation in the 555 is 2.5V x 169mA= 0.42W. It will be pretty warm but not too hot.