How does the wrong gauge electrical wire cause an electrical fire?

The higher the guage the smaller the wire, so the wire could overheat and melt, causing a short and lighting the house on fire

We are talking serving amps. You need to know what the amp demand on all the devices plugged into this lead are.
As I understand the question, you will not be using the plug for the gas dryer, so you are only concerned for the oven.
You didn’t mention if the oven was gas or electric. The electric will have a much higher demand.
The danger is causing a fire. Don’t put a 40 amp breaker on a 12 gauge lead. It should be 20 amps. Get an electrician.

@filmfann
@XOIIO
This was already done to my house for a 40 amp ELECTRIC stove/oven. The guy advertised as an electrician. He said to my face he had a Class A Master Electrician License.

12 AWG will handle 20A. 10AWG, 30 amp in general.
Ampacity is not affected by the length of cable.
Is this a 220VAC application? If so, It needs to be 8–3 romex.
The concern is not for the Stove oven, but for over heating and fire.
I personally would have run 8AWG. Check local code.
There will be some voltage drop. The voltage will be reduced by ~7.5 volts over 75 feet.
This is a voltage drop of about 6.2% if using 120volts or 3.1% if using 240volts.

@blueiiznh
Yes, explain how it overheats and starts a fire and could it potentially affect the gas appliances and blow up my home? Thyank you!

@blueiiznh Thank you for saving me from the type of recall and math that I should not be doing late on a Saturday night!

Okay, the simple version is that whatever you have plugged in is going to do it’s damndest to get however many amps it needs to do what it does regardless of how it’s wired, and if the amp draw is enough to make the wires glow red and ignite your walls then neither the wires nor your appliances will care… but you might.

If you use too small a gauge wire (such as using 12 instead of 8 for a stove), the wire will get hot, the insulation will melt, and the wire will start arcing between the hot and neutral conductors. That arcing will cause a fire.

Also as the wire heats the metal expands, stressing & eventually loosening its attachments at junctions and terminals, which in turn leads to higher current densities, which in turn leads to higher temperatures until insulation melts.

That’s why you shouldn’t mix aluminum and copper wiring. Aluminum expands more than copper, and joints between the two metals become loose from the constant expansion and contraction of the aluminum.