[Build Help] need help fitting this build in my case. motherboard/cooling help

[tb thanks]

so this is my current ideal build
PCPartPicker part list: http://pcpartpicker.com/p/3djn9
CPU: Intel Core i5-4670K 3.4GHz Quad-Core Processor ($189.99 @ Micro Center)
Motherboard: Gigabyte GA-Z87X-HD3 ATX LGA1150 Motherboard ($129.49 @ Newegg)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory ($85.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ Newegg)
Video Card: EVGA GeForce GTX 770 2GB Video Card ($375.91 @ Newegg)
Case: BitFenix Prodigy (White) Mini ITX Tower Case ($69.99 @ Newegg)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($76.30 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.99 @ Newegg)
Monitor: Asus VS238H-P 23.0" Monitor ($139.99 @ Newegg)
Total: $1128.64

i know that the motherboard isn't compatible with the case but this is the case that i have to work out of. this is a gaming computer meant to be for on the go higher end lan gaming. how can i make this compatible without jeopardizing the builds performance? (prob no overclocking intended)
thank you for you help

 

[clarkjd]

First off, you would need to get an ITX form factor motherboard.
See here:
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007627%20600009028%20600438202&IsNodeId=1&name=LGA%201150

 

[tb thanks]

any suggestions on motherboard selection or cooling options?