Should have said no effect on the corrosiveness of the water. I asssume that is what you are concerned with.
If you add demineralized water to another water, the demineralized water addition will simply decrease the water's chemical parameters in proportion to the amount of demineralized water that is added.
For example, add 50% demineralized water, then the hardness, alkalinity, sodium, etc. will decrease 50%.
The addition of demineralized water will in effect increase the cooling tower's COC because the blended incoming water will now be less mineralized.
Demineralized water by itself is corrosive because the water lacks hardness and alkalinity. You typically want a water to be slightly scaling as determined by the Langelier index. However, since you are adding the demineralized water into the cooling tower, the demineralized water will be diluting the chemical content.
It looks like you are planning to add 300 m3/day demineralized water to CT with existing 960 m3/day. That will reduce your incoming water mineral content approximately 1/3 or (300/960 x TDS mg/l).
Cooling tower COC's are typically limited by the hardness, alkalinity, and TSS. You will still have the same limitations.
The water temperature does not appear to be problem. What is your concern with it? You should consider the average water temperature of the blended water across the CT.