A sludge drying apparatus comprising: • a first indirect dryer and a second indirect dryer, each of which comprises: - a casing-like body (3a; 3b) having an inlet (4a; 4b) for the wet sludge, a first outlet (5a; 5b) for the dried sludge, and a second outlet (6a; 6b) for the vapours; - a heating jacket (7a; 7b) fitted at least partially around said casing-like body (3a; 3b); - a rotating mixer (8a; 8b) inside the casing-like body (3a;3b); • a first heating means for heating one of the two jackets (7a, 7b) of the dryers (2a, 2b) so as to impose a pre-drying condition on one of them, i.e. a heating at a temperature comprised between 90°C and 120°C; • a second heating means for heating one of the two jackets (7a, 7b) of the dryers (2a, 2b) so as to impose a drying condition on one of them, i.e. a heating at a temperature comprised between 150°C and 250°C; • a control system configured to impose the pre-drying condition on the first dryer and simultaneously the drying condition on the second dryer, or vice versa, characterized in that said control system comprises first valve means (13a, 13c; 13b, 13d) configured to enable communication of the first heating means with one of the two jackets (7a, 7b) and of the second heating means with the other jacket (7a, 7b), wherein said first valve means (13a, 13c; 13b, 13d) comprise: - a first pair of valves (13a, 13c) associated with the first heating means; - a second pair of valves (13b, 13d) associated with the second heating means, each valve (13a, 13b, 13c, 13d) being disposed in proximity to one of the two jackets (7a, 7b) and configurable in an open position, in which it enables communication between the corresponding heating means (11, 12) and the corresponding jacket (7a, 7b), and a closed position, in which it interrupts said communication, wherein said first heating means is fed with high-temperature vapours generated inside one of the two dryers (2a, 2b) during the drying condition, wherein said first heating means comprises: - a circuit for a heating fluid selectively communicating with the jackets (7a, 7b) by means of said first pair of valves (13a, 13c); - at least one condenser, disposed along said circuit, in which a heat exchange occurs between the high-temperature vapours coming from one of the two dryers (2a, 2b) and the heating fluid. • a first indirect dryer and a second indirect dryer, each of which comprises: - a casing-like body (3a; 3b) having an inlet (4a; 4b) for the wet sludge, a first outlet (5a; 5b) for the dried sludge, and a second outlet (6a; 6b) for the vapours; - a heating jacket (7a; 7b) fitted at least partially around said casing-like body (3a; 3b); - a rotating mixer (8a; 8b) inside the casing-like body (3a;3b); - a casing-like body (3a; 3b) having an inlet (4a; 4b) for the wet sludge, a first outlet (5a; 5b) for the dried sludge, and a second outlet (6a; 6b) for the vapours; - a heating jacket (7a; 7b) fitted at least partially around said casing-like body (3a; 3b); - a rotating mixer (8a; 8b) inside the casing-like body (3a;3b); • a first heating means for heating one of the two jackets (7a, 7b) of the dryers (2a, 2b) so as to impose a pre-drying condition on one of them, i.e. a heating at a temperature comprised between 90°C and 120°C; • a second heating means for heating one of the two jackets (7a, 7b) of the dryers (2a, 2b) so as to impose a drying condition on one of them, i.e. a heating at a temperature comprised between 150°C and 250°C; • a control system configured to impose the pre-drying condition on the first dryer and simultaneously the drying condition on the second dryer, or vice versa, said control system comprises first valve means (13a, 13c; 13b, 13d) configured to enable communication of the first heating means with one of the two jackets (7a, 7b) and of the second heating means with the other jacket (7a, 7b), wherein said first valve means (13a, 13c; 13b, 13d) comprise: - a first pair of valves (13a, 13c) associated with the first heating means; - a second pair of valves (13b, 13d) associated with the second heating means, - a first pair of valves (13a, 13c) associated with the first heating means; - a second pair of valves (13b, 13d) associated with the second heating means, each valve (13a, 13b, 13c, 13d) being disposed in proximity to one of the two jackets (7a, 7b) and configurable in an open position, in which it enables communication between the corresponding heating means (11, 12) and the corresponding jacket (7a, 7b), and a closed position, in which it interrupts said communication, wherein said first heating means is fed with high-temperature vapours generated inside one of the two dryers (2a, 2b) during the drying condition, wherein said first heating means comprises: - a circuit for a heating fluid selectively communicating with the jackets (7a, 7b) by means of said first pair of valves (13a, 13c); - at least one condenser, disposed along said circuit, in which a heat exchange occurs between the high-temperature vapours coming from one of the two dryers (2a, 2b) and the heating fluid. - a circuit for a heating fluid selectively communicating with the jackets (7a, 7b) by means of said first pair of valves (13a, 13c); - at least one condenser, disposed along said circuit, in which a heat exchange occurs between the high-temperature vapours coming from one of the two dryers (2a, 2b) and the heating fluid.