A possible application of nanometer-sized junction arrays is to Coulomb blockade thermometry (CBT), although only highly disordered arrays can be fabricated at present. In this paper, the characteristics of CBT device with disordered arrays will be studied. Similar to what is observed for uniform arrays, there is a dip at zero bias voltage in the differential conductance of disordered arrays. However, the half-width $V_{1/2}$ of the dip for one-dimensional disordered arrays is largely dispersed. This study suggests that better devices can be developed by connecting a number of one-dimensional arrays in parallel to form an array group. The dispersion of half-width is quite small with values of $V_{1/2}$ close to a constant. Further, the effects of electromagnetic environment and low temperature on the half-width are investigated. Results are agreed with those observed experimentally, that for the effect of the environment is negligible for large arrays. The half-width of a disordered array may be bigger or smaller than the ideal value, depending on the extend of disorder.