The ability to strategically reason is important in many competitive environments. In this paper, we examine how relatively mild temporal variations in cognition affect reasoning in the Beauty Contest. The source of temporal cognition variation that we explore is the time-of-day that decisions are made. Our first result is that circadian mismatched subjects (i.e., those making decisions at off-peak time of day) display lower levels of strategic reasoning in the p < 1 Beauty Contest but not in the p > 1 game. This suggests that a cognitively more challenging environment is required for circadian mismatch to harm strategic reasoning. A second result is that choice adaptation or mimicry (i.e., a more automatic type of responding than what is typically considered to be “learning”) during repeated play is not significantly affected by circadian mismatch. This is consistent with the hypothesis that automatic thought is more resilient to cognitive resource depletion than controlled-thought decision making.