Q: my new macbook air 10.7.3 is running hot with the fan blowing just by using the internet. Is there something wrong with the computer?

Check if the sites your accessing are using Adobe Flash, it's a real CPU hog.

My preference is to uninstall Flash from the Mac and use Google Chrome to access those annoying sites that still use flash, as it's got flash built into the browser

I would recommend resetting the SMC, to do so please follow:

SMC RESET

• Shut down the computer.
• Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
• On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
• Release all the keys and the power button at the same time.
• Press the power button to turn on the computer. 

PRAM RESET

• Shut down the computer.
• Locate the following keys on the keyboard: Command, Option, P, and R. You will need to hold these keys down simultaneously in step
• Turn on the computer.
• Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.
• Hold the keys down until the computer restarts and you hear the startup sound for the second time.
• Release the keys.

If the problem persists then contact AppleCare, you have 90 days of free telephone support (assuming you haven't already bought AppleCare), you can find the number in your manual.

Let us know how it goes!

Checked Activity Monitor.  (Applications/Utilities)

AdobeResourceSynchronizer was taking 83% of CPU usage.

Did a google search and found information regarding AdobeResourceSynchronizer causing high CPU usage and heat.

http://forums.adobe.com/thread/822790

Problem seems to be Adobe Resource Synchronizer.app

To disable go to: System Preferences > Accounts

Click the Padlock icon, enter password if needed, click Login Items,

uncheck AdobeResourceSynchronizer

I don't know how this got install on this computer.

I suspect Adobe Reader. AdobeResourceSynchronizer.app is within the Adobe Reader application package.

Control Click (or right click) the Adobe Reader app, click Show Package Contents

Location: Applications/Adobe Reader.app/Contents/Support/AdobeResourceSynchronizer.app

Some other Adobe applications may also cause this to run.

After disabling this in System Preferences > Accounts, temperature seems to be acceptable.

Also start Adobe Reader X, go to Preferences, Tracker and in the "Automatically Check for New Comments and Form Data", slide the top slider all the way to the right so is says Never.

After having done all this and restarted the computer, check Activity Monitor again and see if

AdobeResourceSynchronizer is still running. If it is you can click on it so it is highlighted and click the Quit button in the upper left.

This solved my excess heat problem.

Wow, I tried the SMC Reset, worked like a charm.  Thank you, VERY much.