Fatter wiring

First, if your ALT wire isn't getting hot, it is big enough. A fan load is fairly small (<20 A) compared to max alternator output (>60 A). Even without a fan, the alternator often outputs max to recharge a low battery, so all cars must handle that.

Post #5 is slightly wrong. The ammeter measures current flow in/out of the battery, so a single wire from ammeter to BATT+. The ALT feed splits off between the bulkhead connector and ammeter. It is a "fused junction" wrapped in electrical tape. The schematic shows it as a big "dot". Mine was a bit green from corrosion, and others have had a complete meltdown there. I cleaned and soldered the fused junction.

With corroded firewall connections and a bigger alternator, it is always smart to bypass the ammeter within the engine bay, as recommended. Run a thick wire (~8 awg) from ALT to BATT+. You can tap your fan relay supply from either end or in the middle. If you want to keep your dash ammeter active, you can add a series diode pair that keeps most flow thru the ammeter until it approaches full scale, then shunts around the ammeter. Search for my post for more info.