The spectrum of the zodiacal light is a key for understanding the origin of Solar System dust disk and its connection to dust disks around other planet-forming stellar systems. The 5-16 micron range accessible to the ISOCAM CVF contains both the Wien tail of the spectrum of dust near the Earth and the 10 micron silicate feature, which is now well-observed in many comets and in the dust disk around beta Pictoris. As part of the performance verification phase, the spectrum of the zodiacal light was already measured toward one line of sight (elongation 100 in the ecliptic plane, Reach et al. 1996). We propose here to measure the zodiacal light spectrum in three directions, representing the extremes of its expected variation within the sky visible to ISO. The spectrum toward the lowest and highest solar elongations in the ecliptic plane will be measured in order to determine the spectral variability as a function of distance from the Sun. As the spectrum in the 5-16 micron range is extremely sensitive to the temperature, we expect to detect a large change in spectral shape between these lines of sight and thereby measure the temperature gradient. The spectrum of an ecliptic pole will also be measured, in order to determine whether it is significantly different from the spectra in the midplane of the disk. As asteroidal dust is relatively more confined to low inclinations than cometary dust, we might expect a difference between the minerology of the dust between the plane and pole. Cometary dust is known to produce a strong silicate feature when it is in the cometary coma, and may also exhibit a strong feature in the interplanetary medium.