You have two different problems

If it's smoke you should be able to smell it.

Check the coolant level in the reservoir tank. There is a white plastic fin attached to the rear of the reservoir tank and the coolant should be right at the top of that fin. You want to have 50% of Zerex GO5 anti freeze and distilled water in the cooling system. Finding the leak shouldn't be that hard. Installing a new thermostat isn't difficult. Not being able to look at your car it is hard to tell if a bad thermostat is causing the problem or a split hose is causing the DTC code P0128 to set indicating a problem with the thermostat. Be sure you have a good oring on the cap of the reservoir tank.

You mentioned a hard rain. Water can leak into your car and get into the passenger foot area where under the carpet is the TCU Transmission Control Module. Pull the carpet back remove the white styrofoam and the steel plate by loosen three black plastic nuts. When that steel plate is removed you can easily see the TCU and other modules. Inspect the area for water intrusion. Under the black plastic at the base of the windshield there are four drain holes that if the car is left outside eventually get plugged with leaves and dirt. Remove the windshield wipers, pull the black plastic up ( there are a number of screws you need to remove from the plastic cowl at the firewall in the engine bay) and blow compressed air down those drains to clear them. If they are plugged water gets into the car and will ruin the TCU etc.