def _del_temp(beta, rhat_dot_dgam, dgam0):
    """Returns the small correction in surface temperature

    See Eqn (10) from Jackson+ (2012) ApJ.

    Args:
        beta (float): gravity-darkening exponent, probably 0.07 or 0.25
        rhat_dot_dgam (numpy array): dot product between the unit location
            vector for each grid element of the host's surface
        dgam0 (float): small correction to gravity vector at pole of host

    Returns:
        numpy array: small temperature correction at each point on the
            surface of the host

    """

    return beta*(dgam0 - rhat_dot_dgam)