It didn't behave like this when the car was new. Only started doing this in the last couple of years or so. I also noticed the battery is not fully charged and even died on me so I have to use an external charger to charge it.

 

Voltage is fine. Get your battery tested.
They're only designed to last about 5 years.

 

the temp measurement input is from the ambient air temp sensor. depending on what charge mode you are in it will drop to 13 volts and even down to 12.6 volts if the amp clamp isn't reading a large votage draw from the battery.

if you are getting a slow crank after its parked...I would first rule out the battery( have it conductance tested), then parasitic draw. if no body codes or powertrain codes; then look at the battery amp clamp, its wirings and its input data in the pcm.

 

It's a brand new battery. Even for floating, GM's 13V (if it's true) is too low. I have two chargers, one (Battery Tender) reads 13.31V and the other (Dewalt) 13.88V when floating.
This problem only gets worse in summer time when ambient temperature is high (>80F). I don't see it in winter.

 

Nah. Anything over 12.7V will keep a battery from discharging.

So just to summarize, you said:
- new alternator
- new battery
- battery died once (how do you know?)

Well that tells me you've got a drain, as tech2 says, or something wrong with your starter system. Make sure all the connections are good and tight.

 

Lead battery float charging is to prevent sulfation.
I have undercharged battery when ambient temperature is high, such as in summer.

 

And how does a battery get sulfated? By getting discharged.

It only takes a few minutes @15V (approx) to top up a battery after a normal cranking. After that there is no reason to keep the voltage up high. It just cooks the battery and wastes power. You really think cutting wires under the hood is going to solve your problem?

 

to clarify: the problem is you see the charging voltage is low and this manifests itself how?

 

The problem is now the alternator can't output the correct voltage when temperature is high as shown here:


So at 25C(77F), the voltage limit on recharge should be 14.7V and float voltage at full charge should be 13.8V. It's lowered by about 1V in both cases in my car now. Which means there is something wrong with the control. Constant night driving in hot summer will make this situation worse and eventually drain the battery. But seems nobody knows what controls this or how to fix it.

 

i told you what controls it and what to check.
part of every starting and charging system diagnosis must begin with ruling out the battery. you had no mention of it until post 14. the only other thing I can offer is to perform voltage drop tests of the insulated and grd circuits of the charging system. you should also read the service manual operation & description of the charging system bc depending on what the amp clamp is reading it will not always be at the numbers you posted. betta batteries did not design the charging system mode output. good luck.