Many of today's challenges, such as climate change, war, or health crises, are highly interlinked and intertwined. Actors in the public discourse sometimes use the term "polycrisis" to describe this "causal entanglement of crises". This article investigates whether this entanglement is visible in the media discourse and whether political actors strategically (mis-)use simultaneous and overlapping crises to influence policymaking in favor of their policy beliefs and preferences. Specifically, it studies how the outbreak of the COVID-19 pandemic in 2020 influenced the climate discourse at that time and whether and how political actors included the pandemic as "narrative strategy" to advocate their climate policy beliefs and preferences. To answer this question, this article scrutinizes the climate media discourse in 2020 in Germany and Switzerland and employs a logistic regression model combined with a descriptive and qualitative analysis of the climate discourse in the two countries. Our results show that in both countries primarily pro-environment actors use COVID-19-related arguments as narrative strategy to increase public attention for the need of a more ambitious climate policy, while pro-economy actors follow a strategy of decreasing the salience of the climate issue (i.e., not linking the issues), potentially reducing public pressure for more ambitious climate mitigation.