Recently triple-alpha thermonuclear reaction rate is discussed using some theoretical approaches at low temperature region (below 1 GK), where experimental date is not available. One of them, the calculation via CDCC (Continuum Discretized Coupled Channel) method, in particular, predicts much larger reaction rate by 10^{25} at 0.01 GK, than a standard estimation by NACRE compilation, which is usually utilized for investigating evolutions of stars. It is thus very important to give predictions from other theoretical methods to solve this discrepancy. For this purpose, we introduce a new theoretical approach based on an imaginary-time method, which has an advantage that the knowledge of three-body boundary condition is not required. We show that our results are consistent with the NACRE compilation for whole temperature region from 1 GK to 0.01 GK. We also discuss the reason why the coupled-channel approach gives the much larger reaction rate at low temperature region. This exists in truncation of the channel number adopted for continuum states of 8Be, giving a rise to a large enhancement of the reaction rate at low temperature region.