Op-amp Power Dissipation Calculation for a pulse output
It would be good to have the actual output voltages of each op-amp relative to ground.
But if I interpret correctly you are getting +11V for 22% of the time and -11V for 78% of the time, so there is always a 0.5W dissipation (@0.5A), plus Iq * 12, for a total of 0.62W or 0.74W depending on whether Iq is per amplifier or for both.
So that would be a junction temperature of 65°C at least.