Does the prius c heater work if we set inside temp higher than outside temp ?(Difference is 2 or 3 degrees ). Is the heater take more energy than AC ?
Yes but it might be so small that you won't notice it much. I don't live where the heater is required much but the few times I have used it, it seems rather weak. And I don't think any of the Prii have electric heating elements so the energy use should be much less than the AC.
The "heater" is a valve that allows (hot) coolant from the engine to flow through a small radiator in the interior ventilation system's air flow. Anytime you set ventilation temperature higher than what the cabin temperature currently is, that valve will be allowing coolant, in varying amounts, to flow through that small radiator, to warm the air. The ambient temperature is the outside air temperature. It does have an impact on the cabin air temperature, I mean: if the car's been sitting for some time, ambient and cabin air temperatures are going to be very close. But the ventilation system gets it's marching orders from cabin temperature. Heating requires some energy, nothing is free. For the most part, it's the borrowing of heat from the engine's coolant circuit, which lowers engine temperature, which makes the engine work harder, less efficient. I believe there's also some amount of electrical heating, not sure on that subject tho. In general, heating the cabin tends to have much less impact on efficiency than air conditioning use. The latter requires a compressor to run, putting more load on the engine.
You should expect MPG to drop in colder temperatures for two reasons - slightly longer warm up time for the ICE, and it will come on more often than in the summer months, just to keep the cabin temp up. AC in the Prius C is totally electric and does not require the ICE, so it's effect on MPG should, theoretically, be less than the heater.
Just something to note the C seems to have two ICE temps it tries to maintain. A warm engine temp and a temp to run the heater (which is a higher temp than the warm engine temp). I have tested this several times by turning off the heater and then observing the ICE shut off. Since the ICE toggles on more to keep me warm my mpg went down 5-10mpg. I got some of this back just by only turning on the heater when the ICE was needed for propulsion. I got some more back by partially blocking the radiator. iPhone ?
It starts to have an effect when the engine needs to run extra to provide interior heat. Most of the time, there's enough excess heat in the cooling system to provide enough heat to warm the interior.
I've noticed, if sitting at a red light, with cabin temp set to (say) 20C, and the engine stopped, I can quite reliably get the engine to start, by just ticking the cabin temperature setting up 1 or 2 degrees. Tick it back down: engine goes off.
I'd recommend forgetting about when the ICE comes on. The system is designed to use fuel as efficiently as possible, and the ICE turns on whenever it's necessary to maintain temperature, charge the battery, or provide torque to the drive-train.