Climate change and poorly designed urban development can lead to a number of negative externalities, particularly an increase in the intensity of urban heat islands (UHIs). When combined with an aging population, UHIs can lead to many health problems (mainly heat stress). Reducing these negative impacts of climate change depends not only on the actions of local authorities but also on the actions and attitudes of individuals. Local climate initiatives that improve local climate conditions include paying attention to energy efficiency or supporting initiatives to develop blue–green infrastructure. The aim of our study is to test and explain whether climate knowledge increases respondents’ awareness of their ability to influence local climate conditions. To achieve our goal, a CAWI survey was conducted in May 2024 with a representative sample of 1012 respondents living in different areas of Poland. This country is an inspiring research area due to the carbon-intensive characteristics of the Polish economy, where more than 60% of electricity is still generated from brown and hard coal. In the first part of the survey, respondents’ knowledge about climate change (asking three questions) was verified. Then, via logistic regression, it was tested whether this knowledge could influence respondents’ attitudes toward their ability to influence local climate conditions. According to the results, knowledge of climate change in Polish society is low—only 39% of respondents can correctly identify the cause of global warming. In turn, the results of logistic regression confirm that climate knowledge significantly increases respondents’ awareness of the possibility of shaping local climate conditions.