Note from the paper: They needed water cooling for the MOSFET.
To be fair, it appears that the use of the water-cooling system is only to achieve max power output and not because the transistor would be damaged with only a heat sink, as the authors mention.
You would not be able to operate this thing without some sort of heatsink because 20 W is far too much for a small package like that to dissipate safely. Reviewing the IRFP440 datasheet says that a reasonable heatsink attached with grease (presumably in still air) would result in ~30-40 degree C die temperature rise, which would not be anywhere close to the damage area the transistor but it would result in an increase in Rds and some other things that are important to power output and power handling. It would still work, but efficiency and power output would suffer. I'm not sure but I have a feeling that water-cooling would not be mandatory here. A reasonable heatsink and a fan to move the air over it might get it pretty close to to his published results.
I would put in some thermal shutdown circuit or VSWR protection or whatever for high(er) VSWR conditions if this were meant for radio and not a CVD plasma machine.
In any case, it was an undergrad thought experiment to see if it could be done. In the real world, I'd probably select a transistor that has a bit more thermal headroom. Technology has moved on a lot 1997 so many options.