2004 Toyota Yaris 5-speed automatic won't go in 5th when the engine is cold

Title explains.

The car has a cold engine indicator; when the engine is cold, a blue dashboardlight is shown, indicating that the engine is cold. After driving for a while, the light turns off, meaning the engine is at operating temperature.

While the engine is cold, the car won’t shift to 5th gear, but as soon as the light goes out, the car will shift from 4th to 5th. (If I’m driving an appropriate speed, obviously). This makes me think the systems are somehow connected. (Is it an intended feature?).

About a year ago (when I bought the car), I changed the automatic transmission fluid, because it had too much and because I didn’t know when it was changed last time. I did this my removing the drain plug on the underside of the car. After that I replaced the transmission oil filter, cleaned the oil pan and put it back with a new gasket. Then I filled up the transmission with Toyota Automatic Transmission Fluid Type T IV as this was the recommended fluid to use. Filled it up to the "cold max". I know that this way I only replaced about 1/3 of the fluid.

I don’t think the change of transmission fluid caused this issue, because the previous owner told me about this issue before I changed the fluid. Only he said it doesn’t always happen, but I found this problem happens 100% of the times.

What are the possible causes of this issue?