Not sure what range we can expect in Your country for that pricetag.
My brother recently bought medicore-performance gaming laptop.
Something from LENOVO Y700 series, if i recall well.
i5, 8GB RAM, Nvidia, rather big size, so good cooling seems like.
It was bit over these 700€, but not that much, maybe around 800€. In this case I would recommend saving a bit more and get something good enough.
Can You show some available options on Your market?