What is the rate at which a solute will dissolve into a solvent? Some factors that increase this include: surface area, temperature, pressure, and stirring.
And as you have outlined, the rate of dissolution depends on temperature, intrinsic solubility, rate of stirring, size of solute particles.
And as you have probably realized already some solutes are harder to get into solution than other solutes........Even with flammable solvents you might see a lot of organic chemists giving their slurry a blast with a hair-dryer, or hot air gun to get the last stubborn residue of solute up into solution; and usually they would apply the heat while stirring the solution magnetically. This is a heady mix should you use solvents such as pentane and diethyl ether.
Mind you, most organic labs are now out of the flame age........