## 2 Results
Subsequently, the difference in the growth rates of the inoculated and control plants declined such that at 21 DAI, the inoculated plants displayed only a 65% and a 12% increase under the ambient and high temperatures, respectively (Figure 2f, Table S1). To better understand the RSA, we analyzed the roots according to their root types. The primary roots were negatively affected by the temperature, with the high temperature causing an average length reduction of 41% from that of the ambient temperature throughout the growth period (Figure 2b). The primary roots also responded to the bacterial inoculation at both of the temperature regimes with varying magnitudes. Under the high temperature, the primary root lengths of the inoculated plants maintained an average increase of 154% from that of the control plants; while at the ambient temperature, the stimulation effect of the bacteria decreased from 121% after 9 DAI Figure 2b). At the end of the growing period, the difference in the primary root lengths between the inoculated and the control plants was 3.5 times higher under the high temperature (107%) than it was in the ambient condition (31%). Furthermore, under the ambient condition, the development of the primary roots of both the inoculated and control plants, plateaued after 19 DAI (maximal length of 20 cm as with the plate size), whereas, both the inoculated and control plants showed a linear increase until the end of the experiment under the high-temperature conditions (Figure 2b, Table S1). The growth rates of primary roots also showed a response to the temperature, with the high temperature causing an average reduction of 43% from that of the ambient temperature (until 16 DAI) (Figure 2g). The bacterial inoculation under the high temperature countered this through the stimulation of an increase in the primary root growth rates up until 14 DAI, before the root growth rates rapidly declined. Under the ambient condition, the bacterial application also increased the primary root growth rates; however, the growth rates of the inoculated plants did not change from 9 DAI until 14 DAI, when they started declining (Figure 2g, Table S1). The deleterious effect of the high temperature was especially evident in the length of the 1 st-order laters (from 9 to 21 DAI), with the heat-stressed plants showing an average reduction of 70% from that of the ambient plants (Figure 2c). The inoculated plants showed an increase in the length of the 1 st-order laters under the high-temperature condition. This inoculation effect was present throughout the growth period, although the stimulation effect declined right from the onset of their growth (from 584% to 31%). Under the ambient condition in the beginning, there was increased growth until 12 DAI (103%), after which the stimulation effects decreased (Figure 2c, Table S1). The high temperature caused a decrease in the growth rates of the 1 st-order lateral roots from that of the ambient temperature condition, with an average of 65% (Figure 2h). The increase in the growth rates of the inoculated plants at the high temperature was 584% at 9 DAI, but that declined down to 17% at 19 DAI (Table S1). The control plants, however, showed continuous linear growth rates. At the ambient temperature, the PsJN inoculation caused an increase in the growth rates from that of the control plants up until 12 DAI (by 103%), then this declined afterward. Whilst the control plants showed increasing growth rates until 16 DAI, when their growth rates became constant, the inoculated plants showed an almost linear growth up until 19 DAI, before their growth declined (Figure 2h). The number of 1 st-order lateral roots was reduced in the high temperature condition by an average of 47% from that of the ambient temperature condition (Figure 2e). The bacterial inoculation also influenced the number of the 1 st-order laters, with there being increased numbers from those of the control plants which started to appear at 9 DAI: a 275% increase under the high temperature and a 32% increase under the ambient temperature.