We theoretically and numerically study the effects of thermal noise on pulses in backwards stimulated Brillouin scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise ratio can be significantly improved, or reduced, for specific combinations of waveguide properties and pulse parameters.