There are several factors that will determine how tall a thunderstorm will get. This essay will look at several of these factors.
Height of tropopause: The tropopause acts as a giant cap to convection. This stable layer will slow the updraft and the updraft momentum will eventually halt and the upper level winds will fan out the storm top. The height of the tropopause is different depending on the weather situation. In the summer the tropopause is at a higher elevation. This is because warm air is less dense and occupies a larger volume the thus the troposphere will be taller. The summer and warm season storms will build to a higher altitude since the tropopause cap is at a higher elevation.
Instability release: Instability release determines how fast the updraft is moving. A stronger updraft will allow the storm to build higher into the troposphere. CAPE and LI values are used to assess the updraft strength potential. For example, a storm developing in an environment will CAPE of 3,000 J/kg and an LI of -7 will have a very significant updraft speed. If the updraft speed is intense it will take longer for the updraft to slow down to a halt when it enters the tropopause. These "overshooting tops" can be seen on satellite imagery.
Slanting of updraft: If the updraft can rise at somewhat of a slant it will tend to build to a higher elevation. This slanting of the storm is caused by wind shear. The wind shear allows the updraft and downdraft to separate. When this happens the updraft can sustain itself longer and will not be impeded by the downdraft. It also allows some of the weight of water and ice to be removed from the updraft as it rising high into the troposphere. With less weight the updraft can sustain a higher speed and momentum.
Whether a thunderstorm builds to a modest 40,000 feet or to a significant height of 70,000 feet is going to depend on the factors discussed. It is the warm season severe thunderstorms that have the highest cloud tops since the tropopause is at a high elevation, instability is high and wind shear is significant.