Abstract : The production of transverse energy in deep inelastic scattering is measured as a function of the kinematic variables $x$ and $Q^2$ using the H1 detector at the ep collider HERA. The results are compared to the different predictions based upon two alternative QCD evolution equations, namely the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equations. In a pseudorapidity interval which is central in the hadronic centre of mass system between the current and the proton remnant fragmentation region the produced transverse energy increases with decreasing $x$ for constant $Q^2$. Such a behaviour can be explained with a QCD calculation based upon the BFKL ansatz. The rate of forward jets, proposed as a signature for BFKL dynamics, has been measured.