Even though grease viscosity is depending on working temperature, why do viscosity of some grease increase and viscosity of some grease drops while working under high temperature?
Just like with motor oils, different operating environments require different characteristics of different grease products. For example, some characteristics of the grease to consider are the temperature tolerance and the "shear" qualities. Do tolerances get tighter with operating temperatures? What are the desired "shear" characteristics of the lubricant - essentially the strength of the lubricant before it breaks down? When molybdenum disulfide was all the rage, it was all about preventing metal-to-metal contact when conventional oil broke down. Check out this popular web resource for more discussion on oils and lubricants.