The Space Infrared Telescope Facility (SIRTF) is planned for launch by NASA in 2001 in a heliocentric orbit at 1.01 AU The spacecraft will drift away from the Earth slowly, reaching a distance of 0.3 AU behind the Earth at the end of its 2.5 year mission. This implies that SIRTF will spiral through the Earth's resonant dust ring (Wright et al., 1995) and, in particular, that it will traverse the dust cloud in the ring that trails the Earth in its orbit. We have used a dynamical model of the ring (Dermott et al., 1994) followed by simulation of the SIRTF orbit to predict the variations in the zodiacal thermal emission due to the trailing dust cloud as seen by SIRTF. Because the dust ring is inclined to the ecliptic, the latitude of peak flux of the trailing cloud will have yearly oscillations about the ecliptic. The amplitude of the oscillations will increase as SIRTF approaches the cloud, reaching a maximum of 20 during the mission. The magnitude of the flux variations can be as high as 4 – 5% or 2–3 MJy/Sr, SIRTF's measurements of these effects will allow us to model the number density and thermal characteristics of asteroidal dust particles near the Earth.