We present an experimental study of an integrated slot-waveguide refractive index sensor array fabricated in silicon nitride on silica. We study the temperature dependence of the slot-waveguide ring resonator sensors and find that they show a low temperature dependence of -16.6 pm/K, while at the same time a large refractive index sensitivity of 240 nm per refractive index unit. Furthermore, by using on-chip temperature referencing, a differential temperature sensitivity of only 0.3 pm/K is obtained, without individual sensor calibration. This low value indicates good sensor-to-sensor repeatability, thus enabling use in highly parallel chemical assays. We demonstrate refractive index measurements during temperature drift and show a detection limit of 8.8 x 10-6 refractive index units in a 7 K temperature operating window, without external temperature control. Finally, we suggest the possibility of athermal slot-waveguide sensor design.