Headaches, loss of coordination and confusion are the symptoms that are going to get very serious if one doesn't cool off and hydrate. This is characteristic of heat stroke in the early stages.
What you are describing sounds like heat exhaustion which is the one with the cold clammy skin. Being deprived of sleep does make it easier to develop symptoms. I've only seen it a handful of times throughout my life. Heat Exhaustion is what normally precedes Heat Stroke but the climate here makes it a much faster transition.
You need to find a way to cool off. The US Army recommends a cold shower in the evening for getting rid of excess heat. You need to seek medical attention if your symptoms don't improve soon. I didn't know this was continual, I thought you were just getting sick occasionally. Invest in chemical cold packs and a better first aid kit.
What you are experiencing is more severe than I thought and I'm glad you mentioned it again.