At higher temperatures, do metal wires have a greater chance of short circuiting? I’ve read that short circuiting means that a huge amount of current flows through the conductor in an extremely small period of time.
Also, resistance increases with temperature for conductors, right?
So if temperature increases, resistance increases. Which would mean the current doesn’t have an easy path to flow through. So the wire does heat up, and may eventually cause the fuse to melt or the MCB switch to drop, but there’s no short circuiting, right?
So, assuming the aforementioned definition of short circuiting to be true, and the wire to be isolated (so there’s no chance of any insulation melting and contact with another such wire), am I correct?
 A: 
So, assuming the aforementioned definition of short circuiting to be
true, and the wire to be isolated (so there’s no chance of any
insulation melting and contact with another such wire), am I correct?

Since the most common cause of short-circuits is the failure or shorting of electrical insulation, if there is no chance of insulation failing so that wires will contact each other, then yes you are correct. But keep in mind that we are almost always relying on some form of electrical insulation between live wires. Even air space is considered electrical insulation. When air is being relied upon as electrical insulation we depend on maintaining of that air to prevent short circuits. For example we rely on air between high voltage power lines and between the lines and ground to prevent the lines from shorting and arcing.
So to say that there is "no chance" (zero probability) is a pretty strong statement, since there are numerous ways in which short circuits can occur. The following names a few.
A short-circuit can be the result of overcurrent due to excessive loads on a circuit that are large enough that the heat causes the insulation between conductors to eventually fail (e.g., thermally degrade). Generally this would not occur if a properly sized overcurrent device was used.
A short-circuit can arise due to heating at bad (high resistance) electrical connections. The high heat at the connection may cause failure of insulation between conductors. Because the high resistance is localized at the connection, it does not have much of an effect on the circuit current. High temperatures and arcing at the bad connection can cause insulation to fail and a subsequently result in a  short-circuit. Since the overheating is localized and the current remains near normal levels, normal overcurrent protection does no help. This condition is very difficult to detect and address. Making proper electrical connections is the primary solution. The use of AFCI's (Arc Fault Circuit Interrupters) designed to detect low current may be used detect the arcing and disconnect power.
Hope this helps.
A: In a tungsten filament light bulb, the temperature and resistance rise rapidly until the power being radiated away equals that being supplied.  Normally this occurs at a temperature that is below the melting point of tungsten.
A: yes, your reasoning is correct
A: How much is a "huge" amount of current?
A better definition of a short circuit is a connection where the amount of current flowing isn't well understood by the modeling you are doing.  For most things you are doing, 1000A is a "huge" amount of current.  Staggering in fact.  However, if you are running a conversion station that converts High Voltage DC power lines to AC, 1000A is actually quite small.  They will have modeled the effects of that 1000A while you might not.  Thus, for you, that may be a short, but for them it's standard operating procedures.  Likewise, you may be comfortable with 500mA going through your circuits, but someone making a transistor a few nanometers wide might consider that amount of current to be a "short" because its going to destroy the transistor.
Consider a toaster.  When you push the lever down, you create what would be considered a short: conductors from one side of the wallsocket plug to the other.  And a whole ton of current does indeed go through it.  However, toaster designers modeled this, and chose the length of conductor carefully, controlling the current draw, so that it doesn't flip the breaker.  And, as you note, as it gets hot, its resistance goes up until it reaches a steady state.
Is that still a short?  Depends on how comfortable you are with glowing yellow wires!  The toaster designers clearly planned for it.  And that's what really matters for a short.  When you short things, the assumptions you made about how a circuit works go out the window, and you have to look at new novel limitations (like wires melting, sagging, and breaking).
