Mechanical properties of neurons represent a key factor that determines the functionality of neuronal cells and the formation of neural networks. The main source of mechanical stability for the cell is a biopolymer network of microtubules and actin filaments that form the main components of the cellular cytoskeleton. This biopolymer network is responsible for the growth of neuronal cells as they extend neurites to connect with other neurons, forming the nervous system. Here we present experimental results that combine atomic force microscopy (AFM) and fluorescence microscopy to produce systematic, high-resolution elasticity and fluorescence maps of cortical neurons. This approach allows us to apply external forces to neurons, and to monitor the dynamics of the cell cytoskeleton. We measure how the elastic modulus of neurons changes upon changing the ambient temperature, and identify the cytoskeletal components responsible for these changes. These results demonstrate the importance of taking into account the effect of ambient temperature when measuring the mechanical properties of cells.