In this study, the tasks of thermal equilibrium and heat insulation concept were divided into scientific and everyday contexts to analyzed the level of familiarity, feeling of knowing, state curiosity, and state anxiety that students feel in task contexts and their relationship. The subjects of this study were One hundred nine students in sixth grade of elementary schools located in metropolitan cities. The results of this study were as follows. First, there was no difference in the level of feeling of knowing, state curiosity, and state anxiety in the task of scientific and everyday contexts. In the case of familiarity, there was no consistent tendency in the concept of thermal equilibrium and heat insulation. And the group who recognized the task context familiarly had higher feeling of knowing and lower state anxiety than the group who recognized the task context unfamiliarly. Second, familiarity and feeling of knowing showed high positive correlation, state anxiety and familiarity showed negative correlation, and state anxiety and feeling of knowing had also negative correlation. In addition, familiarity had a negative effect on state anxiety, and FOK had a positive effect on state curiosity and a negative effect on state anxiety. There was no significant moderating effect of the task context. Third, in case of state curiosity, the group perceived the knowledge gap was very small had the highest state curiosity, and the group perceived the knowledge gap was very large had the lowest state curiosity. In case of state anxiety, the less the knowledge gap was perceived, the lower the anxiety was triggered. This study broadens our understanding of the learning process and provides implications for effective instruction strategies for students’ cognitive and emotional states.