Reliable thermometry is normally based on commercial secondary sensors which are factory calibrated. Primary thermometers exist, too, but their use is limited because of intrinsic slowness, complex instrumentation, or inconvenient installation at the desired location. We have found that arrays of nanoscale tunnel junctions exhibit properties which are very suitable for primary and secondary cryogenic thermometry. Temperature range of this Coulomb blockade thermometer (CBT) extends over about two decades for one sensor and the mean temperature is lithographically adjustable. We have studied the performance of the CBT sensors at very low temperatures where the minimum temperature is limited by electron thermalization and at the high temperature end where the finite tunnel barrier effects appear. We have also tested the behaviour of the sensors in a high magnetic field and in radiation.