How it will work if i solder thin wire with thick wire
Well the limiting point here would be motor wires. I would expect whoever designed the motor to have used appropriate wires on the motor so that the loses in the wires are negligible. 

I don't think that in this case it would be a heat problem to connect the speed controller wires to motor wires.

The resistance of wire depends on the length of wire, wire's cross-section and the specific resistance of the wire. The resistance is \$ R= \frac{ \rho l}{A}\$, where A is the area of the cross-section of the wire, l is wire length and \$\rho\$ is specific resistivity of the material. Here is a handy list of resistances of copper wires using the AWG system. Here is a chart with resistances of cables with cross-section expressed in \$mm^2\$.

For exact amount of heat, we'll need the current and the voltage of the motor. The power formula is P=V*I and based on it, we may be able to guess if the wires will heat or not. The exact amount of heat and temperature rise depend on lots of factors such as thermal conductivity between the cable and air and if the cable is being ventilated and so on.