## 1 Introduction  
Dynamic stretching (DS) involves repeated movements throughout the full range of motion (ROM) by contracting the antagonist muscles of the target muscles, such that the target muscles are stretched by reciprocal inhibition [1]. DS is widely performed as a routine warm-up before sports [2; 3]. Previous studies have reported that DS improves the ROM and sports performance [2; 4; 5; 6; 7; 8; 9]. A recent study reported that static stretching (SS) reduces the incidence of musculotendinous injuries during explosive contraction activities such as sprint activities and sports [10]. DS may decrease muscle-tendon unit (MTU) injury rates by increasing muscle strength and MTU compliance, thereby increasing the ability to absorb greater forces and torque [10; 11]. Therefore, DS should be conducted as part of a warm-up before sports [2]. Static stretching (SS) is a type of stretching in which a muscle is held in a stretched position for certain time [12]. Regarding the dose-response relationship between stretching time and ROM, previous studies have found that a longer SS is associated with a wider ROM and lower athletic performance [12; 13]. A recent systematic review by [PERSON] et al. also reported that SS reduces the maximal muscle strength but does not affect jumping or sprinting performance [14]. Short-term SS had little effect on athletic performance [12; 13]. Another study investigated the dose-response relationship between the amount of DS and musculotendinous extensibility [15]. A positive dose-response relationship was observed between the number of repetitions of DS and ROM, although the musculotendinous stiffness (MTS) did not change after one, four, or seven sets of DS [15]. Regarding athletic performance, vertical jump height increased regardless of the amounts of DS when comparing DS for 6 min to DS for 12 min [8]. Furthermore, after one, two, and three sets of DS, sprint times decreased after the first and second sets but increased after the third set [16]. Notably, large amounts of DS may induce fatigue and impair athletic performance. The effects of different amounts of DS on jumping and sprinting performances have been investigated. However, no study has measured muscle strength and temperature simultaneously with the ROM and MTS. Therefore, clarifying the effects of different DS amounts on musculotendinous extensibility and muscle strength and temperature may help determine the optimal DS protocol for improving musculotendinous extensibility and athletic performance within a limited warm-up time. An increase in muscle and/or body temperature induced by repeated DS contractions was positively correlated with athletic performance [17]. Five types of DS with two sets of ten repetitions and six types of DS with two sets of twelve repetitions performed on multiple muscle groups increased core temperature, jump height, and isokinetic knee flexion muscle strength [17; 18]. These findings imply that a larger number of muscle contractions during DS may lead to an increase in muscle temperature, core temperature, and better athletic performance. Moreover, a reduction in MTS and thixotropic effects that increase the ROM are observed with an increase in the muscle temperature. The changes in the ROM and MTS are speculated to be affected by increased muscle and/or core temperatures [19]. Warm-ups before sports are commonly performed using aerobic exercises, stretching, and sport-specific movements [20; 21]. However, the factors contributing to impaired athletic performance after stretching may be caused not only by stretching but also by activities that cause fatigue, such as pre-aerobic exercises [14]. In previous studies that examined the efficacy of DS on athletic performance, aerobic exercise was not performed before DS [22; 23; 24]. Without pre-aerobic exercise, isokinetic knee flexion torque decreased after DS [24]. In contrast, isokinetic knee flexion and extension torque increased when DS was performed followed by aerobic exercise [9].