The International Roadmap for Semiconductors has forecasted a transition from conventional bulk device to silicon-on-insulator (SOI) one, and then to multiple-gate SOI for high-performance devices. Impact of the discrete-dopant number and discrete-dopant position on device characteristics is crucial for nanoscale semiconductor devices. In this paper, the discrete dopant induced electrical and thermal fluctuation of 16nm SOI FinFETs is for the First time explored. A three-dimensional "atomistic" device simulation with quantum hydrodynamic equation is proposed and performed for electrical and thermal characteristics of the discrete dopant fluctuated SOI FinFETs. Discrete dopants are statistically positioned in the 3D channel region to study associated carrier transportation characteristics, concurrently capturing "dopant concentration variation" and "dopant position fluctuation". Effect of the discrete-dopant-number- and discrete-dopant-position-induced fluctuations on device characteristic including variations of the lattice and electron temperatures are advanced. The large-scale computational statistics study provides us an insight into the fluctuation of electrical and thermal characteristics and mechanism of immunity against fluctuation in SOI FinFETs.