How do you manage the summer heat if there is no time to get out of the city? Any suggestions on how to cool down in Manila?

I would suggest a visit to Manila Ocean Park. Escape the summer heat by exploring "Trails to Antarctica". https://www.manilaoceanpark.com/attractions_encounters#ae_1 Walk through the exhibits and have a go at their activities. You will experience being in the snow and probably forgot (for that moment) that you are battling the summer heat in Manila. ;) This attraction is open: Monday to Friday - 10:00AM to 8:00PM Weekends & Holidays - 9:00AM to 8:00PM Last Entry - 7:15PM