Temp Fix Of A Bodge (Blower Motor)

[Niall]

Right so in that case then, your using the wrong size wire and fuse and possibly switch. A fuse won't always 'pop' if it's a steady current. Normally they will only pop if there is a spike (e.g motor blows or there is a short somewhere)
Either way, the bodge clearly isn't safe and needs redoing. Work out the current drawn by the motor and replace the bodge with wiring and components that can handle the current.
As Sam has said, a relay would be a good idea as its a bit concerning that your taking power from the ciggy lighter for something that requires a fair bit of power!