This paper presents a study of hot and cold turbulent jets by using the exact and linearised 'disturbance energy corollaries' proposed by Myers. Myers' energy corollaries are first extended to allow examination of results from Large Eddy Simulations (LES) around a turbulent base flow, via inclusion of additional disturbance energy flux and source terms. The budget of these extended forms of Myers' energy corollaries are then closed on selected LES results from Bodony & Lele. It is argued that Myers' exact disturbance energy flux should become the classical acoustic energy flux in the far-field surrounding a jet issuing into a quiescent domain. Thus, the volume integral of the exact disturbance energy source terms can be considered as related to the sources of far-field sound, although no information on the direction of the generated sound can be obtained using this approach. Moreover, this decomposition does not separate the radiating and non-radiating portions of the sources at a point in space. These claims are partially demonstrated in this paper, with closure of the disturbance energy budget showing that vortical, entropic and 'unresolved scale' source terms are the only significant source terms in this problem. For fixed acoustic Mach number above 0.7, the entropic source term dominates the vortical term for hot jets, which is in keeping with results from other studies on heated jets using acoustic analogies.