I suspect that you have a crack in a printed circuit board of the amp. Cooler weather opens up the printed circuit and then it closes back up with an increase in temperature.I'm having the same problem with my new 2017 Range Rover Sport HSE TD6.
For me, the speakers stop working when the temperature drops below 10 degrees Fahrenheit.
I assume the temperature drop affects the Harmon Kardon amp.
The speakers eventually start working again once the car warms up for ~60 minutes and after I restart the car.
If if stops for good, do a Goggle for Land Rover amp/radio repairs - there is an outfit in the States that know what to fix - kind of a common problem - the crack that is, so you can get your radio going again.
It was chilly up here over Christmas - temps down to -20F for a couple of weeks and -30 for a few days and my radio worked OK; also the heaters fortunately.
Main street is deserted for a reason - local ski area in southern British Columbia, Fernie BC - was cool over Christmas and at home, even cooler.