Leave the thrust alone, just fly the aircraft. Don’t add more complications; the thrust increase will change the rudder requirement, which may feed into roll. Also don’t start introducing ‘what ifs’, the certification rules are such that an engine fire or malfunction is extremely unlikely to damage the wing. History / accident statistics show that we are in far more danger from a poorly flown climb out or a distraction of our own making than for the lack of thrust.
Why get over concerned about pumping 'X' kilos more fuel per second into a burning engine; you (we the industry) are quite happy about climbing to a safe height before completing shut down drills. For those who climb to 1000 ft aal, when on the WAT limit (200 ft/min) that’s 5 min of burning time, which is within most design assumptions and safe.