If the piano is in an air-con room ALL THE TIME, I think the heater bar should be turned off. Otherwise, the air inside the piano will get too dry. If the air-con is only on at night, then maybe it's better to turn it off during the night.
The humidity needs to be fairly constant. Too humid and you run into problems of mould etc. Hence the heater (to dehumidify it). If it's too dry, the wood gets into problem. There's a humidifying/dehumidfying system that some people may install. I believe it includes the heater bar, a water tank, and a humiditystat to monitor the humidity. If you have an expensive piano and want to protect your investment, maybe you should consider one. Otherwise, just try to keep it fairly constant - not too dry and not too humid. Singapore's climate is humid, so I would make sure the heater is on most of the time (except when you have the air-con turned on for long period of time).