## 1 Introduction  
Plants are constantly challenged by an array of biotic and abiotic constraints that limit their growth and productivity. These include environmental stresses such as drought, flooding, extreme temperatures, metal toxicity, and nutrient deficiency, as well as exposure to phytopathogens and herbivorous insects [1]. Climate-related changes, in particular rising global temperatures, are a serious environmental challenge and they are of major concern for future crop production. Temperature plays essential roles in all of the stages of plant development and any exposure outside the optimal range can be stressful or lethal [2]. Plant responses to cope with heat stress vary with the intensity and duration of the elevated temperatures [3]. Aside from directly affecting the plants, increased global temperatures also aggravate other existing abiotic stressors such as salinity, drought, or mineral toxicity [4]. Two general mechanisms for surviving high temperature conditions are employed by plants. Thermomorphogenesis (responses that occur at moderately high temperatures [5]) induces short-term avoidance, e.g., the elongation of the primary roots in search of cooler soil area and water [6; 7; 8] or acclimation, e.g., the changing of the leaf orientation and transpirational cooling through the elongation of the hypocotyl, petioles, and leaves [9; 10; 11]. On the other hand, plants can respond with long-term evolutionary phenological and morphological adaptations [12; 13] that are associated with heat stress. Heat stress occurs when the rise in temperature for a certain duration exceeds a species-specific threshold level [2] that is sufficient to cause irreversible damage to the plants' growth [14]. Plants' morphological responses to elevated temperatures are very dynamic [15]. Developmentsally, these growth parameters are revealed over the lifetime of a plant through various cellular processes, e.g., cell division, cell expansion, and anisotropic growth [15; 16]. While high temperatures have diverse morphological effects on the aboveground plant tissues, such as the scorching of the twigs and leaves along with visual symptoms of sunburn, the senescence of leaves, growth inhibition, and the discoloration of fruits [17]; belowground, they also cause significant modifications to the root system [18]. A moderately elevated temperature leads to root elongation, but this effect stops around 30 \({}^{\circ}\)C, after which the root length decreases [19]. This is reflected in a decreased amount of root growth rate, a decreased meristematic zone at 30 \({}^{\circ}\)C when it is compared to those at 20 \({}^{\circ}\)C or 25 \({}^{\circ}\)C, and a decreased number of cells in the elongation zone of the root. Roots that are grown at 30 \({}^{\circ}\)C also have smaller radii than roots that are grown at 20-25 \({}^{\circ}\)C [19]. Furthermore, another strategy in the RSA to cope with increasing temperatures is the increase in the number and length of the root hairs, which enhances the root surface area for an improved exploration of the soil for water and nutrients [20]. Elevated temperatures often have cumulative effects which result in poor plant growth and performance [4]. Consequently, we require novel approaches to mitigate the plant stress response and meet the agricultural goals under elevated temperatures [21]. Several strategies are already in practice to develop heat-tolerant crop plants, including conventional crop breeding and genetic engineering approaches [22; 23]. The use of plant growth-promoting rhizobacteria (PGPR), in addition to the above, is another strategy that can contribute to agricultural sustainability [24; 25]. Unlike obligate symbionts, PGPR can interact with numerous hosts and improve plant health and stress tolerance through a multitude of mechanisms [26; 27; 28]. PGPR are capable of modulating the root system architecture (RSA), which can significantly affect the crop performance and productivity [29; 30; 31].