How can you expect a "fractional resistance change" with change in temperature? I was learning about temperature dependence of resistance on a website that states as follows.

An intuitive approach to temperature dependence leads one to expect a fractional change in resistance which is proportional to the temperature change

Now my question what makes one to expect there would be a fractional change in resistance with temperature change.
 A: Imagine we could see inside a copper wire resistance in an electrical circuit. We could sketch the copper atoms as circles in fixed positions in some sort of regular pattern. Between the copper atoms we could add a sea of many more much smaller electrons as dots, called conductive or 'free' electrons. (One electron is 1800 times smaller than a single proton or neutron.) When the circuit is connected, the negatively charged electrons drift towards the positive end of the resistor, which is at the end nearest to the positive terminal of the circuit's battery. The copper atoms are fixed, but as the temperature of the resistance increases, the copper atoms vibrate around their fixed positions more and more. The speed and amplitude of their vibration increases the hotter, or more energetic, they become. This vibration scatters the drifting conduction electrons and makes it harder for them to progress through the resistance. So, increasing the temperature increases the resistance to the flow of electrons. It would not be unreasonable to expect that if the temperature is doubled say, then the vibrational energy of the atoms also would double, and so the resistance to the electron drift/flow would roughly double. On the website link in your question, they don't actually explain or show what's going on inside the resistance wire at an atomic level... I hope painting this picture is helpful, all the best.
A: In the classical model, the free electrons are in thermal equilibrium with the atoms of the conductor. They are bouncing around at random between the atoms.  An applied electric field accelerates them (in a direction opposite to the field) between each bounce.  At a higher temperature, they are moving faster, and have less time to be accelerated between each bounce.
