Fast Idle in Cold Start

This is for 2001 Protege ES ( 2.0 Liter, sport type) ( I bought it a few days ago).
 
When  the car is started in a cold morning, the RPM goes up to 2000 and comes down verly slowly.
It takes about 3-5 minitues to reach to normal idle (around 700 RPM).
 
Actually, I am newcomer to US and someone said that this is normal FAST IDLE feature for emssion requirement in U.S.
As for my car in my country, It took 1-2 second to goes to normal idle even in cold start at morning.
 
How about your car?
 
 
 

My 96 ES runs at about 1500 for about a minute or two.  Yours seems to be a bit fast for a bit long. 

In my case, the idle speecd and the engine temperature seems to move in similary pattern.
 
When the temperature reaches to normal, The idle speed also get to the normal condition.
And it takes about 5 minutes in the morning ( these days), and not more than 1 minutes in the daytime.
 
The problem is that when  idle speed is little high, the car is a little noisy and it's not comfortable to drive.
If I start the car when engine is hot enough, the car gets normal idle in 1 second.
 
My former car makes idle to a normal condtion in 2-3 seconds even the engine temperature does not get hot enough. ( This is done by computer which reads the value of engine temperature sensor.) 
 
I wonder that other ESs get to normal idle speed only after the engine temperture gets to normal
OR
the idle speed reaches normal even before the engine temperature get to normal.
 
Looking for valuable comments.  Thanks.
 

That cold idle is a long time.  I timed mine this morning and it was 33 seconds to normal idle speed. It was 50 degrees this morning.  I'm not really sure how this is controlled on your car, but I would get it checked out.  Yours is not right. 

I surveyed protege5 manual and found related article. (Please see the attached one.)
 
I think that, if we assume there is not air intake and idle control problem, the problem is related to ECT sensor or thermostat.
 
I have two possible cases:
 
1) If thermostat is always open, it takes more time to warm up the engine (because it should warm up coolant in radiator, also). So, it takes more time to get to normal idle.
This case, I think, the starting RPM should be normal.
 
2) If ECT reads wrong lower temperature and sends it to ECU, ECU tries to warm up the engine to higher temperature than needed. So, it takes more time.
This case, I think, the starting RPM should be higher.
 
Which one seem reasonable?
 
Anyway, replacing those two parts needs similar procedures and I can replace the two part at the same time. (But, ECT is quite expensive !!!)
 
Any good suggetions? 

I would do the Thermostat first.  It is the cheapest of the two, and, I would think the most likely.