Disastorous biosignal amplifier circuit
Figure 1. The half-supply ground reference circuit is wrong.

You have designed this incorrectly and are applying positive feedback to U2 instead of negative. The LM358 inputs should be swapped. This may not be the reason for your trouble but it can't be helping.

You have drawn the circuit badly and this makes the scheme of what the circuit is doing difficult to decipher. With a better layout you would probably have spotted the error yourself. The typical layout is shown below. Note how higher voltages are generally to the top and lower voltages to the bottom.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. Standard half-supply circuit.

Note that in this layout it is immediately obvious that the non-inverting input is at half supply and that the output is the ground.

Your circuit has C2 and C3 coupled to the op-amp output but this will drive any noise on the supply onto the output so it's not a good idea. Decide which power rail is going to be your reference and tie the capacitor C1 to that rail. This means that if the supply voltage sags the voltage between Vee and your GND will remain constant. C1 looks too small and I would expect something more like 10 to 100 uF in there.

I would expect your error to drive the GND output to Vee. Why this would cause the chip to overheat is not clear to me at this time. Reverse power rails is the most likely cause.