Can I put a laptop Core i7 CPU in a desktop?

You cannot put a notebook CPU in a desktop motherboard. If you want a notebook CPU in your desktop, you basically need to put notebook components in a desk case. There are some companies that do that, but it costs a lot.

What you can probably do is buy a low-end desktop CPU that will have a low TDP. These, however, are likely to have relatively poor performance.

Depending on what your skills are you could retrofit a laptop motherboard into a desktop case.

An easier solution: Some mini ITX boards have socket 988

http://www.commell.com.tw/News/News/News_20100920_LV-67F.htm

http://www.globalspec.com/datasheets/2571/AdvantechIndustrialAutomation/C4B25A4F-7E4E-403B-9009-AF3E8BB89A41

http://jetwaycomputer.com/NF98.html

Mobile CPU sockets don't fit desktop motherbooards (in specification sheets they have a different socket type).

The newest "Sandy Bridge" chips that Intel are about to release (tomorrow) have a TDP of 95 W and the latest benchmarks show that they are very fast indeed with a good performance/watt. They even have half-decent on-board graphics so you don't "need" a discrete GPU unless you want to play games or edit videos.

The new processors are good value for money and you could get away with a very quiet cooler. Titan Fenrir, Thermaltake Frio or something from Noctua spring to mind, with fans set to low speed.