This install enables the oem remote starter in the bcm. The module only acts as a controller that tells the bcm to start or stop.
If the HVAC is "only" blowing cold air, that's because the user settings for the oem remote starter in the bcm, are set to Auto. Vehicle will be kept at 72C. The 4.01 firmware doesn't change any of the factory remote starter settings aside from actually enabling it.
Couple of options:
1. Have the dealer, or someone with a ford scan tool, enable the user menu in the cluster for the oem rmeote starter. You will then have access to change the hvac setting from Auto to Last Used.
2. Do the installation with the FOR2 install instead. Completely different install and requires two keys to program the module.
3. Flash the module for a 2020, with firmware 4.04, and reprogram the module per the 2020 guide. On the 2020 models, the module sets the HVAC to Last Used. It's highly possible the 2020 firmware will work on previous years, but cannot guarantee anything. Worth a shot though.