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We investigate the noise properties of a zero-dimensional InAs quantum dot (QD) embedded in a GaAs-AlAs-GaAs tunneling structure. We observe an approximately linear dependence of the Fano factor and the current as a function of bias voltage. Both effects can be linked to the scanning of the three-dimensional emitter density of states by the QD. At the current step the shape of the Fano factor is mainly determined by the Fermi function of the emitter electrons. The observed voltage and temperature dependence is compared to the results of a master equation approach.