MOSFET gets hot in an Op-amp MOSFET-based constant current load build
This is a linear circuit so of course it isn't turning the MOSFET fully on when maintaining a constant current output.

That means it is dissipating power in the MOSFET. Measure Vds in operation (voltage between pins 2 and 3) and multiply by the current to see how much power you are dissipating.

By matching Vin and the LED string voltage you can reduce that power, but if you want to maintain CC regulation you can't eliminate it, so you have to deal with it using a heatsink.

How are you heatsinking the MOSFET?

Given a certain power - let's say 5W (5V and 1A) - you need a big enough heatsink to dissipate that heat without too high a rise in temperature. Heatsinks are rated in degrees per watt .. so a 5C/Watt heatsink would limit the temperature rise to 25C in our 5W example.

Without a heatsink, you can look up the MOSFET's own thermal resistance (junction to air) in its datasheet : it may be 60C or 100C per watt ... of course that's unsustainable at 5W dissipation. There will be a much lower resistance from junction to heatsink : maybe 1C/W, which you add to the heatsink's own resistance (giving 5C for a total 30C in the example)

The alternative is to abandon this approach and approximate constant current using a PWM controller, which is more complex, but wastes less power by switching the FET properly.