Hi, Jeroen. You're OK on the power supply -- it's good to 36V, or +/-18V. The
LT1678 uses up less than 3.8 mA per channel, so it shouldn't run hot like your
post says.
Go back to the data sheet and get the pinouts on the opamp (it's standard 8-pin
dual opamp). Look at your wiring, check for shorts and miswiring.
Double-check for shorts between the ears. Then double-check your load, and
make sure it doesn't cause excess current draw. Take particular care not to
drive a capacitive load with this op amp. Use an isolating output resistor to
avoid problems. See the data sheet.
http://www.linear.com/pdf/16789f.pdf
If you're still stumped, you might want to look at the possibility that high
frequency oscillations are causing your overheating. Remember the
gain-bandwidth product on this op amp is 20 MHz. You have to be careful with
layout, and be sure to use good high frequency bypass caps. If you're using
one of those plug-in protoboards, that can contribute to your problem. Use a
scope if you have one. With a GBW of 20MHz, just about any scope will allow
you to see the oscillations, if they're there. Use a 10X scope probe if you
have one to minimize ckt. loading. If you do have HF oscillations, change
things to see if it affects amplitude, frequency, &c. The op amp is almost
certainly doing exactly what it's supposed to be doing for the circuit you've
put it in. You just need to find what part of the rest of the circuit isn't
what you want.