Getting this out of the way first: the closer match I've been able to find to that temple is the Shimogamo shrine, which is part of UNESCO's World Heritage List and the location of one of the most popular festivals in Japan, the Hollyhock Festival (Aoi Matsuri) though it isn't a perfect fit.

Now, as for the architecture. Usually, Japanese architecture is divided largely by period rather than give styles especific names (such as Romanesque, Gothic...). Such styles also exist, though not quite as we understand them. The periods are the Asuka and Nara period, Heian period, Kamakura and Muromachi period, Azuchi-Momonara period, Edo period, etc.

Buddhist temples were introduces in Japan during the Asuka and Nara periods, in the 6th century, so we can discard earlier architectures. However, the style didn't fully disconnect itself from Chinese styles until the Heian and Kamakura periods, and it is best represented in the Nanto Sichi Daiji or "Nanto's Seven Great Temples", which are much more subdued in color and size, so we can safely say it isn't that period.

The Kamakura and Muromachi periods are characterized for having a greater military presence and civil unrest, which led to a preference for rustic, non-assuming constructions which, again, disqualify it for this example.

The Heian period is the flourishing time for the Arts. It was also when the color red became more popular, and particularly cinnabar red was also associated with worship, so the shrine's wooden structure was often coated in that shade. The structure became slimmer and more solid materials like mortar and stone started to be used less. The Shimogamo shrine is from that period as well. So, Heian period is the most likely.

There are also construction methods to consider, but it is harder to determine without a full picture of the roof. Considering the entrance is behind Yoshiko, and that the slope of the roof is towards her as well, it would be the hirairi-zukuri type, probably nagare-zukuri (a very asymetrical and slopped roof) but that I can't say with confidence.

Conclusion: from what we see in the picture, the temple would be made with the hirairi method and would belong to the Heian period (8th to 12th century).