Engine gear shift problems in the cold

I bought my 2005 4-door aveo in the summer, and had no issues other than the damn car alarm going off randomly for no apparent reason (which I now know a lot of people have this issue, great job Chevrolet). Now though, whenever it's cold outside and I go to drive my car, it won't switch to the third gear (around 50km/h) until the engine heats up. I took it to a transmission place and they put a really expensive OBD reader to it once it was left outside in the freezing cold one night.. only to find that the scanner came up with no errors. They suggested it was a component in my engine exposed to the elements which tells the computer system in my car what gear it's in and when to switch (he told me this only by driving my car in the cold btw). He said that Chevrolet doesn't carry this part in their inventory and that total cost would be $500 to fix and it wasn't a "guarantee" fix. I have looked at other threads and posts to this issue but none seem to fit exactly to what I having issues with. No garages or transmissions places I have been to have ever experienced or even heard of this problem. Has anyone here had this problem with this or any gear in their car when it's cold or not? It's super frustrating because I have to drive my car around to heat up before I can take it on the highway or else it will rev to 3,500+ rpm at 80-90 km/h putting ware and tare on my vehicle, also wasting a ton of gas. This problems even happens now when it's slightly cold outside and has been sitting out all night.

Anyone insight or help, please let me know. I'd like to get this fixed before next winter.

I have the same issue as well. I took mine to have its transmission fluid flushed and cycled, which helped alot after it was done. Its been a few years since then and the problem still came back. I do one of 2 things, 1: let it idle for 10 mins in the driveway or 2: just drive and let her rev for 2 miles and it finally shifts. The aveo is a good car but chevy ruined all hope for it to be flawless design. A friend also told me that a chevy dealership can reprogram the ecu to shift on-time but when my friend went to have it done they said it wasnt possible.

This isn't an issue, it's on purpose. The transmission does this to protect itself from excessive wear in the cold, it won't shift up beyond 50km+ until the temp needle lifts off.
Many many Japanese transmissions do this.

Mine only on extreme cold days (-20 C and colder) will do the same on the 4th gear. I just drive slowly until it warms up and then no issues. From reading other threads it seems to be a normal occurrence with our cars in cold weather.

As for the alarm problem, it's just the hood switch and maybe a wiring harness that needs to be replaced. There was a TSB at one point for it. I don't know if it's still active. I had the same problem and after they fixed it, it never came back. FYI.

The best thing you can do is let it warm up. Remote starts are like 50 bucks. I'm the mechanic in a Umiat Alaska and we run equipment and trucks hard at -50 colder. Our 1-ton trucks behave the same way until they warm up to a safe operating temperature. Be very gentle with automatics when they're cold. They will burn up and fail if you arn't. I've changed lots of new 1-ton truck trannys from them being ran cold before they've had enough warm up time. Get some transmission flush stuff and follow the directions and run good synthetic fluid with a GM filter. That might help with cold shifting. A 75watt or hotter Kats pan heater from Napa or Walmart and plugging it in at night is also another good thing to do.