During January it can be extremely cold in the touristy places except in Punakha, which is the winter home of the Jekhenpo (Head of Religion — like your holy Pope) and main monastic body. The weather, in Punakha, can be cold in the morning and night but the day would be mild.

Punakha, the old capital, is a one of the most important historical place in Bhutan, of rich culture and warm people.

So, visit Punakha and stay there longer; you could experience the real Bhutan to some extent and have some fun without catching a cold :)

Punakha Dzong; built in the 17th century and arguably the most beautiful dzong (fort) in the country.

An old handmade suspension bridge.

I don't know if the rafting services are open in January.

A village

An old suspension bridge.

Famous Sacred Site of Saint Nagi Rinchen

Drubthob Nagi Rinchen liberated his mother in Punakha.

According to legend, Drubthob Nagi Rinchen (Vanaratna, 1384-1468) a Bengali Pandita and Mahasiddha, reportedly the “last great Indian Pandita to visit Tibet” liberated his mother from the huge black rock in Punakha.

It is believed that he came to Punakha after learning through his clairvoyance power that his mother was reborn as a frog inside the rock, (symbolizing hell) due to her dreadful sins.

The Divine Madman & Phalluses at Chimi Lhakhang

(The Madman of the Dragon Lineage)

Drukpa Kunley was born into the branch of the noble Gya (Bhutanese: རྒྱ, Wylie: rgya) clan of Ralung Monastery in the Tsang region of western Tibet, which was descended from Lhabum (lha 'bum), the second eldest brother of Tsangpa Gyare. His father was Rinchen Zangpo. He was nephew to the 2nd Gyalwang Drukpa and father of Ngawang Tenzin and Zhingkyong Drukdra.

He was known for his crazy methods of enlightening other beings, mostly women, which earned him the title "The Saint of 5,000 Women". Among other things, women would seek his blessing in the form of sex. His intention was to show that it is possible to be enlightened, impart enlightenment, and still lead a very healthy sex life. He demonstrated that celibacy was not necessary for being enlightened. In addition, he wanted to expand the range of means by which enlightenment could be imparted, while adding new evolutionary prospects to the overarching tradition. He is credited with introducing the practice of phallus paintings in Bhutan and placing statues of them on rooftops to drive away evil spirits. Because of this power to awaken unenlightened beings, Kunley's penis is referred to as the "Thunderbolt of Flaming Wisdom" and he himself is known as the "fertility saint". For this reason, women from all around the world visited his monastery to seek his blessing.

Some of his most famous performances include urinating on sacred thankhas, stripping down naked or offering his testicles to a famous Lama. He is one of very few Buddhist teachers to almost always appear in Bhutanese paintings topless. It is known that Drukpa Kunley would not bless anyone who came to seek his guidance and help unless they brought a beautiful woman and a bottle of wine. His fertility temple, Chimi Lhakhang, is today filled with the weaved portable wine bottles.

Visitors to Drukpa Kunley's monastery in Bhutan are welcome to enjoy a short trek up a hill. The monastery is very modest, only one smallish building, but it contains a wood-and-ivory lingam through which one can obtain blessings from the monk in residence.