Disclosed is a method for thermally drying pasty products, in particular wastewater sludge, and a belt dryer implementing such a method. The principle consists of partitioning the drying operations and using, for each of the successive operations, a different quality of air: (i) hot air for “searing” the sludge, (ii) low temperature air, then (iii) cold air for quenching the sludge before the extraction of same. Also proposed are loops of air supply circuits making it possible to optimize the energy consumption of the dryer by reusing energy produced within these circuits. Moreover, the loops make it possible to recover unavoidable low temperature energy or cheap energy, further optimising the consumption of the dryer.