I don't think an older PSU would cause any issues. Power is power. Underpowered PSU on the other hand would cause an issue. As the GPU/any other silicon will try to pull it's rated wattage, if the PSU can't keep up, forces the GPU to pull more current to maintain it's needs. And we all know more current means more heat.
I'd say the users PSU is likely the problem. With the limited context we have.