Intervention could not have been delayed any longer before the building became dangerous.
The grade I listed glasshouse was last restored just 30 years ago but Murphy said the job was not thorough enough to prevent further work, which will see it shut from October until 2018.
Murphy said the Victorian building is "fragile" and all £34m - £14.7m Heritage Lottery Fund cash with the rest from Defra and donations - is needed to save it.
He added that restoration quality has moved on since the early 1980s, when the Queen reopened the restored house. The next set of repairs should last 50 years.
Murphy said Kew's Pagoda is in line for opening to the public in conjunction with Historic Royal Palaces, while the Palm House will need major restoration in 190 years' time.
Construction consultancy Turner & Townsend is managing the job. A temporary 1,200sq m glasshouse will go in front of the 5,000sq m Temperate House while work is going on.
Kew glasshouses manager Greg Redwood is working on a revised plan to restore the old plant layout and raise visitor numbers from the current 500,000 to 700,000 a year.
The adjoining Evolution House will become a public engagement centre, with community and outreach talks, as well as holding weddings that will engage the public and bring in cash.