In this work a didactic path crossing both the life and the works of Joseph Fourier is proposed with the purpose of furnishing an historical reference to some of the most important concepts inherited by him. Particular attention is addressed to the scholars personality features and to the innovative methods and approaches employed in his research which encompassed not only Fourier analysis but also the greenhouse effect and climate science. The didactic proposal, addressed to university students, also includes a simple application of Fourier analysis as well as a comparison with the wavelet approach, this latter representing one of the newest and more interesting development of Fourier analysis.