Actually, pure coolant is less efficient at cooling an engine. In fact, pure water, alone, is best for cooling. The coolant is added to raise the boiling point, not for heat transfer, and as a convenient way to add corrosion inhibitors and, in some cases, some lubrication for the water pump.
I think you need to find out why it was overheating.
I think you need to find out why it was overheating.