tip... it's not k2638, it's 2SK2638 ... that 2S is like the 1N for the diodes (1n4001, 1n5819 etc)
I think the problem is the Vgs (gate threshold voltage) which is 4v typically (3.5 min - 4.5v max). MTP3055 has a Vgs of about 2.5v..
For my own load i use a fqp50n06 that has minimum 2v maximum 4v and it tops at about 3-4A with the opamp I have (a microchip rail to rail one that works only up to about 6v). I used this one because it has a very low Rds(on) of about 0.022 ohm, which is another disappointing parameter of your mosfet , yours has a somewhat large value at 0.65 ohm max, meaning it will get much hotter than others.
You can also improve your load by replacing the 1 ohm resistor with a smaller one... for example you could get several of those 7w-12w axial resistors (white rectangles, cemented) and put them in parallel). The only downside is that you won't have that 1:1 relation between the voltage drop on resistor and the current dissipated on the mosfet.