The events near their extreme values are termed nearly extreme events. The generalized density of states is proposed that is defined by a probability density function. The rate of nearly-extreme events to the total sample size at a given point is the crowding of nearly extreme events, which is an important index used in many fields. Based on the estimation of the generalized state density of nearly extreme events, the parameters of the generalized state density of nearly-extreme anomalous temperature events are constructed with the temperature daily maximum data in summer and daily minimum data recorded in China in winter in 1961-2013. The daily maximum and minimum temperatures recorded at 174 observed stations in 1961-2013 are selected based on the requirement of data continuity from the climate dataset over China, released by the China Meteorological Administration. According to the analysis of the single station Nanjing, the maximum probability density of occurrence about nearly extremely anomalous temperature is marked as max and the corresponding r of max is marked as rp, which indicates that when the difference between nearly extremely anomalous events and extremely anomalous events is rp, the probability of occurrence is maximum. Then rp is defined as the most probable intensity of nearly extremely anomalous temperature events. max and rp can show the crowding degree characteristics about nearly extremely anomalous temperature events and can carry significant physical meanings in the practical application. So the spatial distribution characteristics of max and rp about nearly extremely anomalous temperature events in China in summer and winter are analyzed respectively. In summer, in the west part of Northwest China, South China and south part of Southwest China easily happen the extremely warming events when the most probable intensity of nearly extremely warming temperature event rp values are 1.0℃ and 2.8℃ and the maximum probability density of occurrence about nearly extremely warming temperature max is up to 44%. In South China, south part of Southwest China and Xizang easily occur the extremely cooling events when the most probable intensity of nearly extremely cooling temperature event rp values are 0.5℃ and 2.5℃ and the maximum probability density of occurrence about nearly extremely cooling temperature max is up to 34%. In winter, the warning information about extremely warming events should give to Southwest China when the most probable intensity of nearly extremely warming temperature events rp values are 1℃ and 2℃ and the maximum probability density of occurrence about nearly extremely warming temperature max is up to 32%. The warning information about extremely cooling events should give to Southwest China, South China and south part of the Yangtze River when the most probable intensity of nearly extremely cooling temperature events rp are 1.0℃ and 4.0℃. Therefore, the maximum probability density of occurrence max and the most probable intensity rp of nearly extremely anomalous temperature events can give some early warning information about the coming extremely anomalous temperature events.