Most modern thermocouple readers are temperature compensated and do not require an ice-water cold junction. A simple test to determine if your instrument is functioning correctly, is to short the instrument terminals with an electrical conductor, e.g. copper. The thermocouple reader should read ambient temperature. Deviations from ambient temperature indicate that the instrument needs repair or calibration.
When using a thermocouple, it is very important to understand that the measured voltage is developed along the entire length of the thermocouple. Steep temperature gradients should be avoided since any defect in the wire within the gradient will contribute a large error. Steep gradients may also induce recrystallization and grain growth, thus changing the calibration. In this regard, feeding thermocouples through insulation is critically important since deformation of the wires may produce recrystallization during operation.