The line width of Bloch oscillations has been studied in small capacitance Al-(Al)PbAu Josephson tunnel junctions which were isolated from the low-impedance electromagnetic environment by miniature high-ohmic metallic resistors placed very close to the junctions. Under irradiation by microwaves of frequency f in the range of 300-4000 MHz the I-V curve showed appearance of steps at I = ?? 2ef in correspondence with the Bloch relation. The line width of the oscillations was assumed to be the same as the width of peaks in differential resistance dV/dI under irradiation and was analyzed using a weak-signal response technique. The line width as a function of temperature flattened out at low temperatures and its level depended on frequency and hence on the biasing current. An analysis shows that the line width is basically determined by thermal noise in the resistors and the observed low-temperature plateau can be explained in terms of a hot-electron effect in the resistors.