  We explore dissipative quantum tunnelling, a phenomenon central to various
physical and chemical processes, using a double-well potential model. This
paper aims to bridge gaps in understanding the crossover from thermal
activation to quantum tunnelling, a domain still shrouded in mystery despite
extensive research. We study a Caldeira-Leggett-derived model of quantum
Brownian motion and investigate the Lindblad and stochastic Schr\"{o}dinger
dynamics numerically, seeking to offer new insights into the transition states
in the crossover region. Our study has implications for quantum computing and
understanding fundamental natural processes, highlighting the significance of
quantum effects on transition rates and temperature influences on tunnelling.
  Additionally, we introduce a new model for quantum Brownian motion which
takes Lindblad form and is formulated as a modification of the widely known
model found in Breuer and Petruccione. In our approach, we remove the
zero-temperature singularity resulting in a better description of
low-temperature quantum Brownian motion near a potential minima.
