As I pointed out, you will not see any change in APU parameters. Going to MAX MODE fully opens the APU inlet guide vanes...you can't see that. It may raise the APU TGT as more air goes through the open inlet guide vanes to the load compressor but not necessarily. When you're starting engines, the packs are turned off, galley power is turned off, ATMs are off...the load on the APU is greatly reduced so you may actually see a decrease in TGT.
The only time we ever manually used the MAX MODE spring-loaded position was if we got an INLET FLOW light (probably due to ice forming in the inlet duct) that caused an automatic APU shutdown. After 3-5 minutes and the INLET FLOW light going out, we would then start the APU in MAX MODE.