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yes, temp variation will cause the system to post a message in the DIC intermittently.
It even happened to me, when the temp dropped considerably.
I check my pressures every two weeks, but in the late fall, we had a considerable drop one morning, and the message came on, the chime chimed, but after driving a few miles, the message went out.
The vehicle sat for over eight hours and the temps dropped to the 20s, so when I started the tires were below the minimum set point, and the display lit up. After driving about two miles the message went out, due to the tires warming and the air pressure going up just enough to set off the TPM warning.
Two days later on Saturday AM, before the H3 was driven, I checked the pressures and they were all at 33 psi, but it was in the 40s that day.
So, I have to assume that that morning the system went off, they were at around 29 psi.
I adjusted the pressures, and so far, with checks every two weeks, no more messages.

I believe that GM has issued a bulletin in regard to some porosity problems with some aluminum rims, which is quite common with aluminum rims. However, this would be noticed by someone who is constantly checking their pressures and notes that one wheel assembly drops more pressure than the other wheels, and this would indicate there is a problem with the tire or the porosity of the rim. Easy fix to repair the porosity in the rim since it is at the edge.
My Vette had this problem, and it is sealed by the technician, and after almost three years, never had a problem again.

Now, even if you work or do work for GM, it is not impossible to go to another dealer. Post on this site for another dealer in Phoenix that someone on this forum can recommend. (I have no idea how many dealers there are in your area.)
I know many GM employees who have registered complaints with the assistance center. I did on my Caterra a few years ago, and got it finally fixed correctly.

I can tell you this, there are two things that the dealers are really upset about with new GM vehicles. One, the GM oil change light, took away a lot of their 3000 mile oil change business. Two, the tire air pressure monitoring system.
They are flooded with people who never check their tire pressures, flooding them in the fall with the TPM message, and all that is wrong is the tires are now running low due to the owners not checking or having checked their tire pressure. Since this is not technically a warranty issue, then cannot submit a warranty claim; therefore, they are covering this cost themselves.

Many have their pressures checked at the local oil change shop, and this is one problem. The person drives to the oil change shop, the tires are HOT, the guy doing the checks looks at the tire pressure label, sees 35 psi, and reduces the tire pressures in all tires to 35 psi. (The worse case scenario is this guy thinks all tire pressures should be at 30 psi because the first time he check tires, that was what the first label he looked at stated.)
Tire pressures should only be checked on a tire that has not been driven for at least three hours.
Tires can gain three to four psi while driving on a hot day. (On my Vette, I would gain 4 psi on a hot day in TN. The Vette displayed the pressure in each tire on the DIC.)
So, the guy just reduced the pressures from (let's say) 38 psi to 35 psi; however, after sitting a few hours, the pressure in the tires drops to 32 psi. Temps drop overnight by thirty degrees and now the tires are at 29 psi at startup...system will display a TPM message.
Another problem people to when checking their tire pressures is to check on a day with the sun shining on one side of the vehicle. Direct sunlight can cause the tires in the sunlight to be about two psi higher than those in the shade. So, the person balances out the tires, and those in the sunlight will be lower when the sun disappears.