Case fan amp draw on circuitboard question

Hey, got a quick questions

I bought this mini peltier fridge the other day, and I want to replace a 80mm 1500rpm 12V 0.09A exhast fan with a larger 120mm 1500 12V 0.15A or even better 120mm 3000 rpm 12V 0.25A one.

This circuit board it not connected to a computer power supply in any way, and runs off AC or DC power. The connector for the fan is a standard 2 pin connector found on many PCI peripherals.

So my primary question is, what will happen if i go ahead and try and run 0.15A or 0.25A on a connector currently drawing only 0.09A? I'v heard that this might cause heat to collect on the wire or board since the thickness of the wire determines how many amps can travel across. However all standard case fans seem to use the same wire thickness, so i dunno.

Also, is there any way to check by simply looking at the board?

Any insight would be greatly appreciated.

Thank