Diode Pumped Alkali Laser (DPAL) is one of the main candidates for development of a high power directed energy system producing laser beam from a single aperture with high spatial quality. Currently, several groups in the US and abroad demonstrated DPAL systems with kW level output power and efficiency higher than 50%. At the same time, the DPAL power scaling experiments revealed some limiting effects, which require detailed study to understand the nature of these effects and ways to mitigate them. Examples of such effects are output power degradation in time, alkali cell windows and gain medium contamination and damage that causes lasing efficiency decrease or even lasing termination. These problems can be connected to thermal effects, ionization, chemical interactions between the gain medium components and alkali cells materials. Study of all these and, possibly, other limiting effects and ways to mitigate them is very important for high power DPAL development. In this paper we present our new results of experiments on measurements of the temperature rise in the gain medium of operating DPAL leading to the output power degradation even before visible damage in the gain cell occurs. This degradation can be both recoverable and non-recoverable, depending on operation conditions and the system design.