From what I can find, the package-to-ambient thermal resistance for a DIP-8 is about 70°C/W. A temperature rise of 32°C means the power dissipated is about 0.46 W.
The driver Icc is 6 mA maximum with no load, so the power contribution is 72 mW with Vcc of 12 V. The IRED power with the measured Vf and 5 V through 330 ohms is about 15 mW. The total power dissipation of the driver is therefore about 87 mW and the expected package temperature rise should be about 6°C. Junction to ambient thermal resistance for the package is typically about 110°C/W, so even the die temperature rise should be no more than 10°C. 32°C package temperature rise is far too much (not destructive, but indicative of something being wrong).
I return to the FET temperature rise as an indicator that something is not right. If the gate is being driven with a static 12 volts, the ON resistance of the FET should be no more than about 5 milliohms, and that is allowing for the die being hotter than it should be. 4 amperes and 5 mΩ yield 80 mW. At that power the case temperature rise of the FET should be next to nothing. 10°C rise is far higher than expected, suggesting that either the temperature measurement is wrong or there is significant switching loss because there is some un-detected switching that should not be happening.
If an oscilloscope is not available, put a small capacitor, such as 10 nF, in series with your meter and measure the AC voltage between drain and source of the FET when the FET should be ON in steady-state. It will take a few seconds for meter reading to stabilize, but it should be zero. If it isn't, the FET is switching when no switching is expected. This method can also be used to check the output of the driver.
The driver Icc is 6 mA maximum with no load, so the power contribution is 72 mW with Vcc of 12 V. The IRED power with the measured Vf and 5 V through 330 ohms is about 15 mW. The total power dissipation of the driver is therefore about 87 mW and the expected package temperature rise should be about 6°C. Junction to ambient thermal resistance for the package is typically about 110°C/W, so even the die temperature rise should be no more than 10°C. 32°C package temperature rise is far too much (not destructive, but indicative of something being wrong).
I return to the FET temperature rise as an indicator that something is not right. If the gate is being driven with a static 12 volts, the ON resistance of the FET should be no more than about 5 milliohms, and that is allowing for the die being hotter than it should be. 4 amperes and 5 mΩ yield 80 mW. At that power the case temperature rise of the FET should be next to nothing. 10°C rise is far higher than expected, suggesting that either the temperature measurement is wrong or there is significant switching loss because there is some un-detected switching that should not be happening.
If an oscilloscope is not available, put a small capacitor, such as 10 nF, in series with your meter and measure the AC voltage between drain and source of the FET when the FET should be ON in steady-state. It will take a few seconds for meter reading to stabilize, but it should be zero. If it isn't, the FET is switching when no switching is expected. This method can also be used to check the output of the driver.