The 41-year-old actor, who played Richard 'Boner' Stabone in the 1980s show, was discovered dead in a Vancouver park yesterday after being reported missing last week.
A statement to E! Online said: "The Koenig family thanks you for your kind thoughts at this difficult time.
"It means a lot to them and they are very appreciative of the support they are receiving. Each of these emails will be printed and bound in a rememberance book."
Koenig - the son of Star Trek actor Walter Koenig - is believed to have taken his own life following a battle with depression.
> Stars pay tribute to Andrew Koenig