We present the first experimental results on a spatially‐resolved investigation of a SET (single‐electron tunneling) circuit using the method of low temperature scanning electron microscopy. The new technique can be operated with short electron beam pulses down to 1 μs and small beam current below 1 pA, which gives the value of the charge per pulse as low as one elementary charge. By recording the circuit voltage response to the modulated electron beam irradiation as a function of the beam coordinates on the circuit, we were able to image the potentials of different parts of the circuit. For a SET‐transistor which displayed the Coulomb blockade we found evidence of memory‐effects due to charge trapping in the vicinity of one of the junctions. Further possible applications of our method for the spatially resolved study of single‐electron circuits are suggested.