And I am venturing that "I lost my temper" can cover a multitude of actions. It will depend on what the OP did after losing temper that will decide whether or not he is approved for unemployment insurance. I once heard someone describe their actions as "I lost my temper" and when we got the employer's statement, this temper outburst had actually involved taking hostages and a stand off with the police.
No, OP you cannot justify your behavior which led to your firing as being because you were sick and tired of the alleged illegal behavior of your employer. You have the choice to quit, you have the choice to report your employer's behavior to authorities, but you do not have the choice of throwing some sort of tantrum and having all forgiven when you tell the unemployment hearing officer that the employer was allowing illegal activity to go on in the worksite. After all, it's sort of like accusing your soon to be ex spouse of molesting your child, isn't it? If it has happened for a long period of time and you're only bringing it up now, you were apparently okay with it until now. It does not justify the actions that got you fired.
What they will have to decide is whether the behavior you exhibited when you lost your temper rises to the level of gross misconduct. This means it was something so inappropriate that you should have known it was wrong to do even one time, even without the employer giving you warnings, writing you up and giving you a chance to change your behavior or not repeat it. Muttering an epithet under your breath and throwing down a dish cloth, that's maybe minor enough not to be considered gross misconduct. Throwing a tray of glassware on the floor, screaming curses at your supervisor, or punching out a co-worker? That's gross misconduct, and can get you fired, without approval for unemployment insurance.
If I were you I wouldn't even, in the course of this hearing you're about to have, even bring up and try to justify yourself because your employer's illegal activity. Because the unemployment system is not in the business of enforcing any other kind of law, they will not care what your employer is doing or how incensed you were about it. They just want the facts about the actual incident that led to your firing. They'll go with which of the two of you, you or the employer, is most believable in describing the events that took place. They'll decide if your actions rise to the level of gross misconduct, and by this, whether or not your employer was justified for terminating you or whether or not they should have reasonably overlooked your behavior and given you another chance.