We conducted an experiment causally manipulating reliance on more intuitive vs. more deliberative behavior through time pressure and time delay. Our design uses a novel manipulation which relies on gradual economic incentives and was devised to avoid the high degree of non-compliance observed in previous experiments. The “social heuristic hypothesis,” which claims that people are intuitively predisposed to cooperate, is not supported in our data. On the aggregate, subjects are not more cooperative under gradually-incentivized time pressure. We also measured individual attitudes on social values and attitudes toward interpersonal risk, and find that both correlate with the tendency to cooperate. A detailed analysis suggests that subjects with a stronger (resp. weaker) prosocial predisposition become more (resp. less) cooperative under time pressure compared to time delay, although the effect is only noticeable for extreme-enough predispositions. A possible interpretation is that relying on more intuitive behavior enhances individual heterogeneous predispositions, while relying on more deliberative behavior moderates them. This suggests that tendencies toward cooperation might not be universal, and rather be moderated by individual characteristics.