Former world No.1 Murray, who has spent several seasons dealing with hip problems and recovering from surgeries, gave Thiem some words of encouragement at the end of their clash at the Caja Magica.
Alize Cornet won hearts at the Melbourne Park after giving an emotional tribute to former player Jelena Dokic during a post-match interview after her victory against Simona Halep in Australian Open fourth round
Both players struggled as the temperatures hit 33 Celsius (91 Fahrenheit) on Rod Laver Arena, but it was the 32-year-old who prevailed 6-4, 3-6, 6-4 in a gruelling 2hr 33min.
World No.2 and title favourite Daniil Medvedev won over the Australian Open crowd on Saturday as he eased into the last 16 along with Stefanos Tsitsipas.
Former world number one Simona Halep laboured into the Australian Open second round after an error-strewn clash with Poland's Magdalena Frech which saw 11 service breaks.
Former world number one Simona Halep's first title win in 16 months in Melbourne at the weekend saw her jump five places to 15th in the WTA rankings released on Monday.
A fit-again Simona Halep stormed to her first title in 16 months when she downed Russian Veronika Kudermetova to clinch the Melbourne Summer Set crown on Sunday.
Naomi Osaka pulled out of a warm-up tournament for the Australian Open on Saturday, saying her "body got a shock" after playing her first matches for four months.
Naomi Osaka defeated Andrea Petkovic 6-1, 7-5 to set up a semi-final against third seeded Russian Veronika Kudermetova.
Naomi Osaka will be playing for the first time since her US Open exit. Simona Halep will be aiming to build a resurgence after an injury-struck 2021. Meanwhile, Emma Raducanu will be competing in her fourth tournament since winning the US Open.