The quantum thermal bath (QTB) method introduces zero-point motion in molecular dynamics simulations via a Langevin equation with a colored random force. This approach can be efficient for a variety of chemical and condensed-matter problems, but it suffers from zero-point energy leakage (ZPEL), as many other semiclassical methods. In this contribution, we present a quantitative criterion that allows detecting and quantifying the ZPEL in QTB simulations, based on deviations from the quantum fluctuation-dissipation theorem (FDT). These deviations can be monitored along the QTB trajectory and they provide a very general diagnosis tool for the ZPEL, without resorting to normal mode calculations. We will then build on this criterion to describe an adaptive QTB approach in which the quantum FDT is strictly enforced via an on-the-fly, spectrally resolved fine tuning of the system-bath coupling. The basic principle of the adaptive method is as follows : at high frequencies, the damping is reduced and the power injected by the bath (via the random force) is increased, while the reverse is done at low frequencies. This fine tuning is performed during the dynamics in order to compensate the ZPEL exactly, as measured by the FDT criterion. We finally illustrate the performances of the adaptive method on different model and more realistic systems that exhibit strong ZPEL in standard QTB simulations and analyze how efficiently this leakage can be cured in the proposed adaptive framework.