The idea behind this build is to provide support to your allies. This build is not meant to function well as a demigod killer, but as a means to deal mass damage against multiple foes and control lanes.
Level 1: Rain of Ice I
Level 2: Permafrost I
Level 3: Circle of Fire I
Level 4: Rain of Ice II
Level 5: Fire Aura I
Level 6: Frost Nova I
Level 7: Rain of Ice III
Level 8: Circle of Fire II
Level 9: Circle of Fire III
Level 10: Rain of Ice IV
Level 11: Circle of Fire IV
Level 12: Deep Freeze I
Level 13: Frost Nova II
Level 14: (Save)
Level 15: Biting Chill, Frost Nova III
Level 16: Deep Freeze II
Level 17: Deep Freeze III
Level 18: Deep Freeze IV
Level 19: Inspirational Flame
Level 20: Permafrost II
Circle of fire is chosen instead of Fireball for area of effect damage, and also because deep freeze is not meant to be used as a damaging effect: you want to maintain those debuffs on your opponents so your allies can more easily kill them. Upgrading this to rank 4 is debatable, as it only provides 1 more second of 'silence' per rank and enhanced attributes could very well be selected instead.
Starting Items: Banded Mail, Scale Mail
Item 2: Unbreakable Boots 1500
Item 3: Boots of Speed 1000
Item 4: Nimoth Chest Plate 1500
Item 5: Heart of Life 4250
Item 7: Wand of Speed 1250
Item 8: Groffling Warplate 5200 (Sell Scale Mail)
Total: 14380
Other Stuff:
Item xx: Deathbringer 20000
Item xx: Mage Slayer 7560 (Sell banded Mail)
Item xx: All-Father's Ring 23800 (Sell Unbreakable Boots)
Favor:
Blade of the Serpent
Always keep mana potions handy until you obtain the heart of life, just in case your blade is on cooldown. Try to cast circle of fire pre-emptively and switch to ice mode prior to your opponents actually reaching you. Hide behind towers and do not engage unless there are other demigods around. Your job is primarily to soften up other demigods and keep them running back to their crystal to heal. This build is =not= effective against less than 3v3 matches.
Hope that helps ^^
PS-You are retarded if you think listing artifacts makes these items a requirement of the build.