Not talking about any player specifically, but conversely a player who "raises his game" during garbage time or in meaningless games isn't typically, without more, considered a player who plays with heart. But why not? The guy is trying hard even when the games don't matter. Never give up attitude!
I think that makes some sense to me. There's less of a barrier to overcome to raise your game in those situations because nobody else is trying that hard, so it's less impressive. If you do that every game including the important ones, then you DO get credit for that consistency/constant drive and are considered a player who plays with heart, and if you only do that in the games that don't matter, it shows that your priorities are all out of order AND you don't have a never give up attitude.
There is something to be said for the guys who give 100% every shift/game no matter the situation and just don't have the skill to raise their game further in the playoffs (and actually regress in comparison), though. But I don't know that they aren't associated with having heart either. For example, nobody questions Jannik Hansen's heart and work ethic, but it doesn't really translate as well into success when everyone else raises their work ethic in the games that matter compared to when the games don't matter (Hansen sometimes offensively dominates in preseason games and meaningless games in a way that he can't in the playoffs).
Did you have examples in mind of guys who only play well in games that don't matter but get unfairly maligned when they deserve to be viewed as having a lot of heart? I can't think of any.