。
How are you coping with this heat wave?
Literal
Heat-wave [object-を] how are-enduring?
しのぐ ('to endure, to get through, to tide over') is an evocative verb covering 'to survive a hardship' — often paired with heat, cold, difficulty, or poverty. Here it's in ~ている form for 'are you currently coping?' どう as the interrogative adverb 'how.' 猛暑 ('scorching heat') is a fixed meteorological term now widely used for summer heatwaves in Japan.