In the absence of simple noninvasive measurements, the knowledge of temporal and spatial variations of axons mechanics remains scarce. By extending thermal fluctuation spectroscopy (TFS) to long protrusions, we determine the transverse amplitude thermal fluctuation spectra that allow direct and simultaneous access to three key mechanics parameters: axial tension, bending flexural rigidity and plasma membrane tension. To test our model, we use PC12 cell protrusions-a well-know biophysical model of axons-in order to simplify the biological system under scope. For instance, axial and plasma membrane tension are found in the range of nano Newton and tens of pico Newtons per micron respectively. Furthermore, our results shows that the TFS technique is capable to distinguish quasi-identical protrusions. Another advantage of our approach is the time resolved nature of the measurements. Indeed, in the case of long term experiments on PC12 protrusions, TFS has revealed large temporal, correlated variations of the protrusion mechanics, displaying extraordinary feedback control over the axial tension in order to maintain a constant tension value.