A thermal-infrared image of comet Giacobini-Zinner has been used to determine the spatial distribution of dust grains in the Comet's coma. In the present paper we emphasize the results of this imaging which bear on the expected impact rate of dust grains on the International Cometary Explorer (ICE). the expected impact rate is calculated for a range of grain radii. For particle sizes comparable to those inferred for most comets, the impact rate is on the order of several hundred per second. This rate is in agreement with the predictions by Divine (1985), but it is more than two orders of magnitude larger than the rate observed by ICE if the observed impacts were on the spacecraft body. However, the observed impact rate is roughly comparable to that inferred from our infrared imaging if, as suggested by Gurnett et al. (this issue), the impacts were on the ICE antennae, which had a much smaller cross-sectional area than the spacecraft body.