Does wrong current strength settings in pin planner can cause FPGA heating problem?

Hi,
what means heating problem for you? How much power consumption? How much overtemperature? Excessive current consumption in core or IO supply lines?

To ensure that overheating isn't caused by defective FPGA, does the supply current reduce to low values if the device is unconfigured?

Most likely cause for high power consumption is shorted output. In this case drive strength plays a role.

Another possible reason for high power consumption is running many logic cells and registers at maximum frequency.

I don't discuss trvial reasons like exceeded supply voltage.