Interesting... Once the engine has run for 15 mins or so.... there should have been a lowering of the charging voltage coming from the alternator....
The BTS sends a signal to the ECU, the ECU controls the charge rate of the alternator to the battery and supplies the vehicles electronic components trying to maintain a preset system voltage.
When the battery is cold the alternator charges at a higher rate and as the battery warms up the charge rate slowly drops to the preset factory voltage.
IF there is a problem with the BTS or if the sensor is disconnected; that would affect the alternator charge rate depending upon the factories default set point.
IF you feel comfortable... measure the voltage at the alternator charging stud while testing to see if there is a difference then at the battery.