AD811AN Op-Amp working temperature?
This amplifier is designed to operated in a specific fashion with specific feedback resistor values.  Note that the In+ and In- terminals have very different characteristics.  Operating the device un-connected w/o feedback circuits it is unsurprising that it has problems.  To guess what is happening would be just that, guessing.  Connect it up with the recommended values, Do not leave the input floating (it will pick up stray fields and amplify those and chew up more current doing so) and then if it's over-heating come back and ask the same question.

These devices can run hot.  the quiescent current (taking worst case @ +/- 15 V) is 18 mA.  This is dropped across 2*12 = 24 V => 0.432 W of dissipation.  in a DIP package it it 90 C/W from ambient 39 C + 25 C (room temp) = 64 C even before it is driving anything.