Answer: It will make no difference.
Explanation: For an object to float or sink in a fluid, there is a force called buoyancy force acting on it.
Buoyancy force is an upward force experienced by the object due to the fluid. Its magnitude is calculated by the formula:
where:
is density of the fluid
V is volume of the object
g is gravity
The steel ball is free falling, so, there is gravitational force acting on it.
Since it is falling into the water as well, there will be buoyant force acting against the gravitational one. But none of the forces is dependent on water temperature so that variable won't change the falling.
So, temperature will make no difference.