Why engine revs higher in Neutral after cold start?

I’m puzzled: On my way to work today, the 1st red light–just 1.3 mile from my apt.–

was a long one, so I shifted my '97 car’s auto.trans from D into Neutral. The engine immediately revved much higher,& I thought:

Boy, it’s really drinking the gas now. All I “know” is that engines are set to rev higher & warm up quickly because, at higher

operating temperature, combustion is more complete & various exhaust pollutants are minimized.

Question: If, at the stoplight, I leave it in Drive with the brake on, is the engine running slower (& using less gas), or is it

actually revving higher but the auto.trans

muffles the sound? If it runs slower in Drive, then that will save the most gas, right?

Do you feel your car has a problem or are you analyzing it’s cold operating parameters?

Your car is not fuel efficient when cold for various reasons.

If the idle speed does not return to “normal” very quickly (even before the temp gague reaches it’s “normal” operating point) you have a problem that needs to be looked at.

If a '97 ‘free wheels’ at a noticeably higher RPM when 1.3 miles from your home than it does when fully warmed up, something is wrong. Probably nothing serious, but the car is not getting to normal operation as quickly as it should. If it starts to do it all the time (warm or cold), then suspect a cracked air tube or a dirty idle air control valve or a dirty throttle valve.

With regard to the question of whether the engine is actually turning faster in neutral, if it sounds faster, it is faster, but it is tough to say whether it is burning more fuel. If engaging the transmission loads the engine significantly, then it has to add more air and fuel to maintain the lower RPM than it would to maintain the higher ‘free wheeling’ RPM. If the car remains stationary or barely creeps when you take your foot off the brake, then the fuel consumption is probably about the same in either state.

No, I don’t think there’s any problem–I’m just curious about how it works & want to save gas. Note: I made a mistake: the 1st stoplight is only 1/3 mile from my apt., so it was still warming up.(I get going immediately after I start the engine.)
As I sat at the light in N, I listened carefully, & the engine did slow down slightly, so I think all is well.