Bridge Configuration Problems for OPA2544
If it is overheating without a load, it may be oscillating. Long wires to the IC can create parasitic issues. Try a 100 pF cap across the feedback resistors (C2 and C3 in my schematic). Put it very close to the IC. This will limit the bandwidth, but it should still be sufficient for your application.

If your actual load is anywhere near 30 ohms, I believe that you have underestimated the opamp power dissipation.


The dissipated power can be calculated, but it is easier for me to simulate. The power dissipated in each opamp is equal to the voltage drop from the rail to output, multiplied by the resistor current. This is only valid for the positive cycle, but since everything is symmetrical, that is all you need to simulate.
The opamp drop is 35V minus 1/2 of the output voltage. Since the circuit is symmetrical, there is a virtual ground half way through the resistor.
I ran the simulation using your original input parameters, +/- 10V sine.
Since you have 2 opamps in the package, the total package power will be twice what is shown in the bottom graph blue plot. My initial rough calculation (in comments) is too low, your heatsink needs to be even larger than I initially said.



simulate this circuit &ndash; Schematic created using CircuitLab