Heero is the Perfect Soldier, as he possesses the qualities therein. He has no emotion or supresses them very well. His fighting skills and capabilities are top notch. His intelligence is off the charts. And most important, he is not afraid of death. The Perfect Soldier.
There have only been some very rare displays of Heero's emotions, or what little emotoins he has. One such example is towards the beginning of the Gundam Wing series (I'm not sure which episode), where OZ is out to destroy Relena Dorlian (Peacecraft). Heero protects her with Gundam Zero, though he doesn't know why. Even when he is feeling compassion, perhaps even affection for another person, he doesn't realize what it is- he doesn't understand it. That is just how unfamiliar he is with experiencing emotion.
Perhaps Heero goes too far with his role as the Perfect Soldier (how many times have we seen him adopt the death glare and say "Omae o korosu"? ^_^ ). However, Heero does get the job done, completing his mission at any cost. Heero is the most dedicated pilot to his duties, no sacrifice too large to complete his task- very important qualities during those times of war found in the Gundam Wing series.
It is, though, in fanfiction, amusing to portray Heero's seriousness in a comic manner, which can be hilarious at times. It is always fun to make the Perfect Soldier have a small, almost silly fault. Examples would be a love for Duo, perhaps. There are many fanfics written that pair Heero and Duo, with Heero's one weakness as Duo.
Though Heero can be portrayed rather comically at times, his role is a most serious and important one, for the Perfect Soldier is needed to bring peace to the colonies and the Earth in the Gundam Wing series.