Does temperature affect electrolysis of CuSO4 to make copper?

No idea what was the investigation you did, so it is hard to comment on.

In general - things definitely change with temperature. If the changes are small, they can be masked by the experimental errors. My bet is that is the case here.

Of things that definitely change - see the Nernst equation, it has a temperature dependent term. Changes are small, and in the controlled current experiments completely irrelevant - but they do exist.

Usually, these sorts of questions, "What is wrong with my experiment" tend to go nowhere on this board.  This time, you've gotten good answers.  Use the Nernst equation, plugging in your various temperatures, and see how your measured parameter (what was that, I can't tell) could theoretically change.  If that change is less than you can measure, that should satisfy your instructor.  Note that in the formula:  http://en.wikipedia.org/wiki/Nernst_equation#Expression  temperature is in the numerator, multiplied by a power function.  You should be able to see an effect, but how much of one will depend on how much temperature difference there was, and what you're able to measure.

Temperature has an effect on the quality of the plated copper. Higher temperature accelerate chemical reaction, so the deposit is very rough and non ductile.