Unless your a geek or just curious, you can skip my answer.
All materials have certain properties that are known and the value of the change in size of a material due to temperature is called its Coefficient of Thermal Expansion (COTE). This value is multiplied by the degrees of temperature change and the answer is in either inches or millimeters.
The Coefficient of Thermal Expansion for pure lead for temperature changes in Fahrenheit and the answer in inches is 16.3 millionths of an inch per degree temperature change per inch of length or size.
The standard temperature for distance measurement is 20 degrees C. or 68 degrees F. so that number has to be subtracted from the temperature you want to know the answer for.
Say you want to know how much lead will expand at its melting point of 618°F. Subtracting 68° from 618°, the temperature change value is 550°F. 550 times 16.3 millionths of an inch = .0090 inches per inch of length.
If you are talking about a ball or bullet that is 1/2" in diameter, you would multiply the .0090 expansion value by 0.500 which gives a growth size of .0045 inches so, the cavity in the mold needs to be .5045 in diameter when it is heated to 618°F .
Now, you can't just use this value to get a .500 diameter bullet because the mold is also going to expand when it gets hot. Due to this, the Coefficient of Thermal Expansion value for the mold material must also be known and taken into account.
If the mold is steel, it's COTE is 8.4 millionths of an inch per degree F per inch of thickness.
Knowing the temperature of the mold when it is up to casting temperature will be fairly close to the temperature of the solidifying lead, we can use the 550°F, value to figure out how much the mold will grow. 550°F X 8.4 millionths = .0046 per inch growth per inch times the .500 bullet diameter = .0023 inches.
Because the steel mold expands less than the lead expands, we have to make the mold at room temperature, larger than the finished bullet size. The difference in size between the two materials is .0045 (lead) - .0023 (steel) = .0022 so, if we make the bullet mold .5022 in diameter at 68°F it should produce a lead bullet that is .500 in diameter.
By the way, the COTE for aluminum is about 13.2 millionths of an inch per inch so it is very close to the COTE of lead. This means a aluminum mold will grow just about the same as the lead so, an aluminum mold can be almost exactly the same size at room temperature as the bullet will be at the same room temperature.
Now, aren't you sorry you asked the question? I know some of our members are.