Microscopic characteristics of an aqueous excess proton in a wide range of thermodynamic states, from low density amorphous ices (down to 100 K) to high temperature liquids under the critical point (up to 600 K), placed inside hydrophobic graphene slabs at the nanometric scale (with interplate distances between 3.1 and 0.7 nm wide) have been analyzed by means of molecular dynamics simulations. Water-proton and carbon-proton forces were modeled with a multistate empirical valence bond method. Densities between 0.07 and 0.02 1/Å^3 have been considered. As a general trend, we observed a competition between effects of confinement and temperature on structure and dynamical properties of the lone proton. Confinement has strong influence on the local structure of the proton, whereas the main effect of temperature on proton properties is observed on its dynamics, with significant variation of proton transfer rates, proton diffusion coefficients, and characteristic frequencies of vibrational motions. Proton transfer is an activated process with energy barriers between 1 and 10 kJ/mol for both proton transfer and diffusion, depending of the temperature range considered and also on the interplate distance. Arrhenius-like behavior of the transfer rates and of proton diffusion are clearly observed for states above 100 K. Spectral densities of proton species indicated that in all states Zundel-like and Eigen-like complexes survive at some extent.