The TPMS will light up if any tire drops 25% of it's pressure. Tire pressures change roughly 1PSI for ever 10F change in temperature. So yes, a 20F drop could cause TMPS to alert you.

What should your tire pressure be? Well you will get many answers. The door jam says 32PSI. The manual says 35PSI if driven at higher speeds. I have run mine at 42PSI on the front and 40PSI on the rears for over 25,000 miles. Tire wear is very even. Tread depth is at 7/32 on all four, and was 10/32 when I bought the TCH.

I find 32PSI gives a "squishy" ride - when cornering, tire roll affects handling. At 40PSI the TCH handles like a different car, much improved cornering and braking. The tires also last longer at 40PSI.

In my opinion, Toyota recommends 32PSI for a soft, comfy ride, not for handling or tire wear.