We study numerically the thermodynamic properties of the spin nematic phases in a magnetic field in the spin-1 bilinear-biquadratic model. When the field is applied, the phase transition temperature once goes up and then decreases rapidly toward zero, which is detected by the peak-shift in the specific heat. The underlying mechanism of the reentrant behavior is the entropic effect. In a weak field the high temperature paramagnetic phase rapidly loses its entropy while the ferroquadrupolar nematic phase remains robust by modifying the shape of the ferroquadrupolar moment. This feature serves as a fingerprint of generic ferroquadrupolar phases, while it is not observed for the case of antiferroquadrupoles.
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