Not quite sorted yet then....
Ok, Winter or summer use has little bearing in this instance, if your amps will overheat in summer, then chances are they will in winter....
The main issue with amplifier heat build up is the increase in internal resistance of many component parts, the hotter an amp runs, the lower the output power will be....The most common cause of heat build up is poor setup....
You should also ensure your amplifiers gain/sensitivity control is correctly set to match your head units pre-out voltage....
An amplifiers heat sink is designed to keep the amp cool at full power, the only time your amp will achieve this is playing a 0dB tone whilst receiving a 14.4v power supply, which in the real world equates to 'never'....
The issue of the Head Unit remote feed is quite simple, it is simply a 12v feed which carries very little current, add multiple items and the current drops, as the current drops so will the voltage, adding any kind of current draw to this circuit will simply kill the voltage, low voltage equates to amps simply not switching on....
You then need to consider fusing options for the Head Unit remote, I tend to fuse both behind the Head Unit, (2amp fuse), & in the boot area before distribution, (again a 2amp fuse), just to be sure....
With regards simply powering the fans from the amps Batt feed, I wouldn't personally as this could introduce noise from the fan itself or possible ground loop issues....
With regards fan wiring;
Wired in 'Parallel' they will both run in unison, both pushing or both pulling....
Wired in 'Series' they will run against each other, one pushing, one pulling....
For best results the airflow should be along the heat sink rather than across it, (end to end rather than front to rear)....
A quick pic, (wired in 'Parallel);
