We propose the skewness of mean transverse momentum, $langle p_t rangle$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $langle p_t rangle$ distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that $langle p_t rangle$ fluctuations have positive skew, which is significantly larger than if particles were emitted independently. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of $langle p_t rangle$ to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of $langle p_t rangle$ fluctuations is a generic prediction of hydrodynamic models.
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