Control PTC heater with mosfet
It is not possible to determine if your project "will burn down your house" with the information you have provided, but it is very unlikely. Your fireplace gets hotter and it has not burned your house!

At any rate, you are not using that much power (250 Watts, max.), but you must keep it contained and away from flammable materials, off course!  

If you can't solder, you can use crimps and terminal strips!

An example of how to determine the wire size needed.  Assume the heater voltage is 25V and the current required is 10A (250W), this means the heater's resistance is 2.5 ohms.  In order for the wire to "not melt," it should have less that .25 ohms (1/10th).  You now look at a chart that shows the ampacity of cables with a give length and diameter, and a resistance of less than .25 ohms.

I would guess that a 3 foot length of 10 AWG should do the job.
Don't forget to heat-sink your FET.

Mount a terminal strip to your PCB, connect thick cables to terminal strip via screws.  PCB should have thick lands plating under the terminal strip that connect with mounting screws.