Machine and method for hot testing test pieces made of a thermoplastic polymer, in which the test pieces are immersed in a tank full of a heat transfer liquid which is heated; a fan generates, immediately above the tank, an air flow to carry away volatile substances emitted by the tank and the air flow is made to pass through a filtering cartridge housed removably inside a first chamber delimited by a casing, which is provided with an inlet opening, that faces towards the tank and is arranged flush with or immediately above an upper perimetral edge of the tank; the air flow is made to pass sequentially through at least three filtering elements, which are arranged hydraulically in series, including: a pre-filter; at least one activated carbon filter; and a HEPA filter; an hour counter signals when the time has come to replace the filtering cartridge.