Recent high-resolution spectra of z ~ 2 quasars suggest that Lyα clouds may have much lower temperatures (T~5000 K) than previously thought (T~30000 K). This result is very uncertain at present, and there are still considerable differences between different groups of observers. In this paper we perform calculations based on the standard pressure- confined model of Lyα clouds in order to test the possibility of obtaining such low temperatures. Our results suggest that it may be difficult to explain temperatures as low as 5000 K using the standard pressure-confined model of the clouds. We also give many observational predictions which may in the future allow the accuracy of the model to be tested.