An electrical submersible pump for pumping well fluid from a well, comprising: a tubular pump housing having a longitudinal axis and a housing bore that is coaxial with the axis; a plurality of centrifugal pump stages in the housing bore, each of the stages having an impeller and a diffuser; a rotatable shaft mounted on the axis within the housing for rotating the impellers; a non-rotatable bearing mounted in the housing, the bearing having a shaft passage through which the shaft extends; a sensor hole (53, 55) extending through the housing and into the bearing, the sensor hole (53, 55) having a bearing sensor hole portion extending within the bearing; and a temperature sensor located within the sensor hole (53, 55); the housing comprising a cylindrical body and a base having a base bore in which the bearing is mounted, the base having a neck of a smaller outer diameter than an upper portion of the base defining a downward facing shoulder, the sensor hole (53, 55) having a base sensor hole portion extending upward and inward from the downward facing shoulder toward the longitudinal axis and being aligned with the bearing sensor hole portion; a sensor line connected with the sensor and extending from the base for transmitting a signal from the sensor; and a conical section in the base bore extending downward and inward from a cylindrical section in the base bore; wherein the bearing is mounted in the cylindrical section of the base bore, and the conical section extends downward from the bearing; and a lower end of the bearing sensor hole portion is spaced from an upper end of the base sensor hole portion by a gap. a tubular pump housing having a longitudinal axis and a housing bore that is coaxial with the axis; a plurality of centrifugal pump stages in the housing bore, each of the stages having an impeller and a diffuser; a rotatable shaft mounted on the axis within the housing for rotating the impellers; a non-rotatable bearing mounted in the housing, the bearing having a shaft passage through which the shaft extends; a sensor hole (53, 55) extending through the housing and into the bearing, the sensor hole (53, 55) having a bearing sensor hole portion extending within the bearing; and a temperature sensor located within the sensor hole (53, 55); the housing comprising a cylindrical body and a base having a base bore in which the bearing is mounted, the base having a neck of a smaller outer diameter than an upper portion of the base defining a downward facing shoulder, the sensor hole (53, 55) having a base sensor hole portion extending upward and inward from the downward facing shoulder toward the longitudinal axis and being aligned with the bearing sensor hole portion; a sensor line connected with the sensor and extending from the base for transmitting a signal from the sensor; and a conical section in the base bore extending downward and inward from a cylindrical section in the base bore; wherein the bearing is mounted in the cylindrical section of the base bore, and the conical section extends downward from the bearing; and a lower end of the bearing sensor hole portion is spaced from an upper end of the base sensor hole portion by a gap.