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