## 1 Introduction  
Numerous non-linear systems include the quadratic and cubic non-linearities simultaneously, such as the cable [1], shallow arch [2], arch-foundation structure [3], cable-stayed beam [4], multi-cable-stayed beam [5], beam-cable-beam [6], sagged-cable-crosstie systems [7, 8], and cable net structures [9], etc. Particularly, the cable is one of the most vital structural elements that exhibits slenderness, exceptional flexibility, and ultra-low damping simultaneously [10]. Therefore, several previous studies have highlighted dynamic characteristics of the inclined [11] and suspended cables [12], and the linear and non-linear dynamics of suspended cables subjected to parametric and auto-parametric excitations have been discussed in detail. Meanwhile, another significant resonant response is the modal coupling between a cable's different modes. To explore various types of internal resonances, such as in-plane/out-of-plane and symmetric/anti-symmetric modes, a combination of perturbation, numerical, and experimental methods have been utilized. By employing these techniques, one aims to gain a comprehensive understanding of the system dynamics and uncover any underlying non-linear behavior [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. As a result, different types of bifurcations and chaos mechanisms can occur due to the planar and non-planar modal interactions, the localization of energy and its conversion from the in-plane mode to the out-of-plane one, and vice versa, are observed due to the non-linearity [28, 29]. Apart from the various short/long-terms excitations and natural/human-made disasters, the cable structures always suffer from many environmental factors. Among these disturbances, temperature changes can have significant effects on dynamic behaviors [30], particularly the cable structures [31]. Understanding their dynamical behaviors including thermal effects is critical and significant in the practical engineering. Provided that the temperature effects are not distinguished correctly and appropriately, it may result in false-positive or false-negative damage signals [32]. Furthermore, even considering a single cable, some previous studies have shown that temperature variations can significantly affect its static and dynamic characteristics [33; 34; 35; 36; 37]. In recent times, significant attention has been paid to studying the non-linear vibration behavior of suspended cables that experience both single and multi-harmonic excitations in thermal conditions [38; 39; 40; 41; 42; 43]. These studies aim to provide a deeper understanding of the system dynamics and the impact of thermal effects on the cable's behavior under different types of excitations. It is observed that many interesting non-linear phenomena are induced due to temperature changes. Nevertheless, a single-degree-of-freedom model has been used in some previous studies [38; 39; 40; 41; 42; 43], and the modal interactions are all neglected for simplicity. Since multiple modes are included, the internal resonant responses cannot be ignored. Understanding the temperature effects on the internal resonant responses of suspended cables is crucial for their successful application in various practical engineering structures. Impressive qualitative and quantitative discrepancies, e.g., extra Hopf bifurcations and chaotic motions, are observed due to temperature changes in the planar two-to-one internal resonances [44]. Nevertheless, if the coupled motions are extended from planar to non-planar ones, the internal resonance refers to some notable energy exchanges between the in-plane and out-of-plane components due to non-linear coupling. To the best of our knowledge, there is no previous study of thermal effects on the complex non-planar non-linear phenomena (resonant responses, static and dynamic bifurcations, and non-planar coupled motions, etc.) before. For these reasons, the investigation here is viewed as a significant extension from the planar coupled motions to the non-planar ones.