Online fake news can have noxious consequences. Social media platforms are experimenting with different interventions to curb fake news' spread, often employing them simultaneously. However, research investigating the interaction of these interventions is limited. Here, we use the heuristic-systematic model of information processing (HSM) as a theoretical framework to jointly test two interventions against fake news that are implemented at scale by social media platforms: (1) adding warning labels from fact checkers to initiate systematic processing and (2) removing social endorsement cues (e.g., engagement counts) to reduce the influence of this heuristic cue. Moreover, we accounted for dispositions previously found to affect a person's response to fake news through motivated reasoning or cognitive style. An online experiment in Germany (N = 571) confirmed that warning labels reduced the perceived credibility of a fake news post exaggerating the consequences of climate change. Warning labels also lowered the (self-reported) likelihood to amplify fake news. Removing social endorsement cues did not have an effect. In line with research on motivated reasoning, left-leaning individuals perceived the climate fake news to be more credible and reported a higher likelihood to amplify it. Supporting research on cognitive style, participants with lower educational levels and a less analytic thinking style also reported a higher likelihood of amplification. Elaboration likelihood was associated only with age, involvement, and political leaning, but not affected by warning labels. Our findings contribute to the mounting evidence for the effectiveness of warning labels while questioning their relevance for systematic processing.