Ibrox was maybe a few degrees short of the Mexican heatwave Reyna could have been enjoying on the other side of the world had it not been for his dogmatic manager, Dick Advocaat, but you could hardly tell from the glow the little American midfielder wore after his first goal for Rangers allowed the champions to squeeze past Kilmarnock on the opening day of their defence of the Scottish Premier League title.
Reyna's strike certainly brought a glow to the 48,000 home fans, although most of them came prepared with one of their own as Glasgow basked in temperatures of 80F as Scotland's league season embraced July for the first time in living memory. It was shorts (Nike replica ones, naturally) for the boys, and halternecks for the girls. The smell of Ambre Solaire overwhelmed that of the hot dogs, and the souvenir traders had no chance of shifting those woollen scarves.
Not that Reyna was complaining. "It was hot out there," he smiled, "but that's what I'm used to. I heard it was all rain and grey clouds here!"
Give it time, Claudio. The boy from New Jersey only arrived in Glasgow four months ago after a pounds 1.2m move from German side, VfL Wolfsburg, and one of the first questions he had to fence off at his press conference was how he could dovetail his commitments to Rangers and to his country.
On Saturday, he found out. While his United States team-mates were defeating Germany 2-0 under the Guadalajara sun in the Confederations Cup, Reyna was stuck in Govan.
Advocaat may previously have been the Netherlands' national manager, but he has seen how long-distance commuting has affected other clubs as their players have gone off across the world to play for their countries.
"I was supposed to be with the US team," explained Reyna, "but Dick spoke to our coach, Bruce Arena, last week and they came to an agreement. Since the guys [US] beat Germany, maybe they won't call on me in the future," he smiled.
Little chance of that, if Arena sees the tape of the 68th-minute winner, in which Reyna took a pass from Jorg Albertz and thrashed it on the run past Kilmarnock goalkeeper, Colin Meldrum, from a tight angle. The relief inside Ibrox was tangible.
Ally Mitchell's excellent equaliser three minutes earlier, exposing Craig Moore's defensive frailties, had threatened to give Kilmarnock a deserved point after coming back from Rod Wallace's sublime opener.
Goals:1-0 Wallace, 38; 1-1 Mitchell, 65; 2-1 Reyna, 68.
Rangers (4-4-2): Klos; Adamczuk, Amoruso (Vidmar, 81), Moore (Porrini, 66) Numan; Reyna, Ferguson, Van Bronckhorst, Albertz; Amato (Johansson, 70), Wallace. Substitutes not used: Niemi, Nicholson
Kilmarnock (3-5-2): Meldrum; McGowne, Dindeleux, Innes; McPherson, Reilly, Holt, Hay, Mitchell; Roberts (Vareille, 59), Jeffrey. Substitutes not used: Stewart, Fowler, McCutcheon
Referee: M Clark (Edinburgh).
Man of the match: Reyna.
Attendance: 48,074.Reuse content