The last eight showdown got underway at 5pm local time (4pm BST) but the sun began to set in the second set.
That meant those watching at home had to deal with a frustrating shadow drawing across the court making visibility ever the more difficult.
Federer won the first set 6-3 but midway through he second Thiem was cast into darkness and fans were only able to see Federer’s shots.
“I can barely see Thiem on the shadow side of the court #CajaTrágica,” one supporter wrote on Twitter.
And another added: “Really struggling to catch all of the action on one side of the court.”
A further user commented: “Impressed with Federer but is Thiem even on the court?”
Amazon Prime tennis commentator also pointed out the difficult conditions – which only continued to get worse.
“Who is at the most difficult end at the moment?” she said.
“Some players really don’t like the ball coming out of the shade and it is a deep shade here.
“A big contrast between the two sides of the court.
“Some players don’t like it coming out into the light.
“The shadow will probably take 50 minutes to get across the court and it is caused by the retractable roof.”
Federer and Thiem are fighting for a semi-final clash with world No 1 Novak Djokovic.
The Serbian was handed a bye in his quarter-final earlier today because Marin Cilic withdrew with food poisoning.