Land surface temperature plays an important role in the water cycle and surface energy balance. Using data collected by a vorticity covariance tower from 2010 to 2022, the relative threshold method and TRM method were employed to study the land–atmosphere exchange of water and the heat flux of rubber forest ecosystems under heatwave and non-heatwave conditions. The results show that the latent heat flux, sensible heat flux, and incoming and outgoing radiation increase from non-heatwave to heatwave conditions. In addition, the multi-year average LST was 6.7 °C higher under HW conditions than under non-HW conditions at the 99% confidence level. Further attribution analysis demonstrates that heatwave-induced land surface temperature change is mainly governed by atmospheric factors rather than by land surface factors. Specifically, radiative forcing shows the largest positive contribution, which is partly offset by the negative contributions of air temperature and relative humidity. In particular, the contributions of radiative forcing, air temperature, relative humidity, and atmospheric pressure to LST were 14.70 K, −4.76 K, −5.86 K, and −0.04 K, respectively. Moreover, surface resistance contributed to LST by 2.42 K, aerodynamic resistance by −0.23 K, and soil heat flux by −0.91 K.