The electrical resistance of mats of single-wall carbon nanotubes (SWNTs) is measured as afunction of mat temperature under various helium pressures, in vacuum and in atmosphericair. The objective of this paper is to study the thermal stability of SWNTs produced in ahelium arc discharge in the experimental conditions close to natural conditions of SWNTgrowth in an arc, using a furnace instead of an arc discharge. For each testedcondition, there is a temperature threshold at which the mat’s resistance reachesits minimum. The threshold value depends on the helium pressure. An increaseof the temperature above the temperature threshold leads to the destructionof SWNT bundles at a certain critical temperature. For instance, the criticaltemperature is about 1100 K in the case of helium background at a pressure of about500 Torr. Based on experimental data on critical temperature it is suggested thatSWNTs produced by an anodic arc discharge and collected in the web area outsidethe arc plasma most likely originate from the arc discharge peripheral region.