Thermocouple insulation operating temperature is always an issue. If the insulation used 'melts off' then the two couple wires will short anywhere along their length where the insulation is gone, causing the measurement point to 'move' to the point where insulation is still functional and they may not be at the same temperature as the end of the TC.
There are two maximum temperature ratings for a typical thermocouple, one is the basic limit of the metal wires used which is fixed in value as defined by being a type J or K or R, etc. The second limit which is lower is the insulation used to separate the two wires from each other except at the very end where they are shorted together that being the 'measurement point'. One can buy couples with special mineral insulation or physical separating the wires with ceramic beads with two holes to keep the wires separated. But yes if the insulation is exposed to temperature higher then their rating then if will effect the reading.
Omega Engineering is a very good source of technical information for TC and other temperature sensorshttp://www.omega.com/thermocouples.html