As cooler temperatures consigned this week's heatwave to memory, Federer swept past Russia's world number 79 Teymuraz Gabashvili 6-2, 6-2, 6-3 in what is his record 57th consecutive major tournament.
Federer, with an unsurpassed 17 Grand Slam titles but now aged 32, last year lost in Wimbledon's second round and in the last 16 at the US Open, raising doubt about his ability to win more major titles.
"It was a tough year last year and it took some time to figure out what I needed to do to feel better and to get my confidence back, because that's what I thought it was mostly," said Federer, seeded six.
"For the last four to five months I feel that I'm back to normal again and at least I feel I've done the work to catch up and haven't had any setbacks, so it's very positive."
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"I didn't have the best of Wimbledon and US Opens last year, and I didn't want to get ahead of myself," the four-time champion said.
"Now the draw is getting extremely difficult, regardless of whether it is Jo-Wilfried or Gilles, but I'm looking forward to it... I've done the work and haven't lost a set so far."
Wimbledon champion Andy Murray continued his recovery from back surgery with another fluent win, downing Feliciano Lopez 7-6 (7/2), 6-4, 6-2 to reach the fourth round.