## 5 Conclusions  
In this study, analytical solutions to the various relative-scale media are derived, including infinite and semi-infinite ones. Dimensionless parameters are designed to reveal the temperature evolution regularities from the heating mechanism. Some conclusions are made below:  
1. The temperature field evolution is the comprehensive result of dimensionless parameters \(\gamma\), \(\beta\), \(\omega\) and \(\Theta_{0}\). In general, the smaller the distance away from the heat source, the shorter the time intervals brought by larger velocity, the lower the relative intensity of boundary-convective heat transfer and the higher the initial temperature, the greater the benefit will be to heat accumulation and temperature rise. Among which, the most important influence factor can be \(\gamma\), as the regions far away from the point heat source are little impacted. 2. The periodically reciprocating motion of point heat source results in surplus temperature appearing as a special feature, oscillating around the stable time-averaged quantity. For an infinite medium, the surplus is symmetrical about the horizontal coordinate at \(\xi=\beta/4\). The maximum temperature value is obtained at the same location, but the peak value of fluctuation amplitude appears outside the abscissa interval [0, \(\beta/2\)], the regions of maximum surplus temperature and most violent fluctuation amplitude are abhorrent. 3. The reduced parameter \(\beta\) has a critical influence on temperature distribution, the amplitude of temperature fluctuation, the time to reach steady-state and the stable time-averaged quantity. In the regions of an infinite medium where temperature fluctuation is not obvious, surplus temperature reaches a steady state more quickly, and the stable time-averaged quantity is larger when the reduced parameter \(\beta\) increases. 4. Only if some specific conditions are satisfied, such as adiabatic boundary and neglecting the influence of the initial temperature, the analytical solutions to the temperature field of the semi-infinite media degenerate into a similar form to these infinite media. Studies on the temperature evolution mechanism help further enrich the moving heat source theory and have great potential to provide theoretical guidance for engineering practice, such as in the fields of welding, heat exchangers and so on. [PERSON] and [PERSON] proposed the idea of this work. [PERSON] made main contributions to the derivation of specific formulas and he wrote numerical algorithm programs in Matlab with the help of [PERSON], [PERSON] and [PERSON] are responsible for the edition and analysis of the numerical results. [PERSON] finally reviewed and checked the whole article. All authors have read and agreed to the published version of the manuscript. This research was founded by National Key Research and Development Plan, grant number No. 2019 YFB2006402. **Acknowledgments:** [PERSON] wants to express his thanks to his wife and lovely daughter for their financial and spiritual support during the study for his doctorate. Your selfless help is his motivation for constantly researching in this field. **Conflicts of Interest:** The author(s) declared no potential conflict of interest with respect to the research, authorship, and/or publication of this article. The authors declare that they have no conflict of interest.