While thermal therapy is increasingly applied in clinics, real-time temperature monitoring in the target tissue can facilitate improvements in the planning, controlling, and evaluating of therapeutic procedures. Thermal strain imaging (TSI), based on tracking the echo shifts in ultrasound images, has great potential for temperature estimation as is demonstrated in vitro. However, due to physiological motion-induced artifacts and estimation errors, employing TSI for in vivo thermometry is still challenging. Building on our earlier development of respiration-separated TSI (RS-TSI), a multithread TSI (MT-TSI) approach is proposed as the first part of a bigger plan. A flag image frame is first identified by analyzing the correlation between ultrasound images. Then, the quasi-periodic phase profile of respiration is determined and split into multiple parallelly distributed periodical subranges. Multiple threads of independent TSI calculations are thus established, with image matching, motion compensation, and thermal strain estimation performed in each thread. Finally, after applying temporal extrapolation, spatial alignment, and interthread noise suppression, the TSI results obtained in different threads are averaged to obtain the merged output. In microwave (MW) heating experiments targeting porcine perirenal fat, the thermometry accuracy of MT-TSI is comparable to that of RS-TSI, while the former exhibits lower noise and higher temporal density.