Temperature gauge fluctuating? Almost overheating when commuting far

So my Mom left my Honda Civic lights on all night which killed the battery and later on my car started to overheat due to fan not working anymore. When the car overheated I ran it like 5 minutes on red without water to get home. My dad told me the heads are fine. We replaced the fan, hoses, temperature sensors on the car however the temperature fluctuates from high to low. Sometimes gets hotter when I'm not moving. It just randomly goes up and down and sometimes is stable. When I'm commuting about 20 miles away from home the temperature will get really hot on arriving my destination like the engine slowly heats us gradually. Sometimes I hear like pressurized air escaping from the radiator cap. We don't have the thermostat installed since it broke. What is the problem?