A new molecular dynamics algorithm is introduced for sampling the canonical distribution. The method rescales particle velocities using a random factor to ensure the correct kinetic energy distribution. The algorithm is formally justified and shows that a conserved quantity exists, which can be used to assess sampling accuracy. The method is tested on Lennard-Jones and TIP4P water models in solid and liquid phases, showing excellent performance and independence from thermostat parameters. The algorithm is an extension of the Berendsen thermostat with a random force to enforce the correct kinetic energy distribution. It allows for a conserved quantity similar to energy in the microcanonical ensemble, which can be used to verify sampling accuracy. The method is compared with other thermostats, including Nosé-Hoover, and is shown to be more ergodic. The algorithm is also tested for dynamic properties, showing accurate results for energy fluctuations and diffusion coefficients. The method is simple to implement and has been shown to be effective for both small and large systems. The algorithm is also shown to be robust against finite time-step errors and can be extended to other stochastic molecular dynamics methods. The results demonstrate that the new thermostat samples the canonical ensemble accurately and efficiently.A new molecular dynamics algorithm is introduced for sampling the canonical distribution. The method rescales particle velocities using a random factor to ensure the correct kinetic energy distribution. The algorithm is formally justified and shows that a conserved quantity exists, which can be used to assess sampling accuracy. The method is tested on Lennard-Jones and TIP4P water models in solid and liquid phases, showing excellent performance and independence from thermostat parameters. The algorithm is an extension of the Berendsen thermostat with a random force to enforce the correct kinetic energy distribution. It allows for a conserved quantity similar to energy in the microcanonical ensemble, which can be used to verify sampling accuracy. The method is compared with other thermostats, including Nosé-Hoover, and is shown to be more ergodic. The algorithm is also tested for dynamic properties, showing accurate results for energy fluctuations and diffusion coefficients. The method is simple to implement and has been shown to be effective for both small and large systems. The algorithm is also shown to be robust against finite time-step errors and can be extended to other stochastic molecular dynamics methods. The results demonstrate that the new thermostat samples the canonical ensemble accurately and efficiently.