Sets of rules are proposed that allow one to write down the amplitude associated with a diagram at temperature [ital T], once the energy running around each loop has been summed over, in the imaginary-time formalism. Alternative forms are given: one is based on tree diagrams, another one on possible intermediate states. A close analogy to the [ital T]=0 case is obtained. The amplitude's analytic structure is explicit. A factorization property is found for the [ital N]-point imaginary-time Green functions.