According to the paper, it's the absolute temperature that matters. The desorption is optimal at about 60°C to 70°C, meaning the absorption-desoprition cycle wouldn't work anymore if the ambient temperature is too high. The absorption phase took place at 25°C ambient - the provided data suggests that the desorption would dominate over the absorption above about 50°C.

In conclusion, if the environment is 50°C or hotter, the sponge cannot absorb much water from the atmosphere, because the kinetics imply that the water would evaporate too quickly.