Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If someone prays, believing or thinking that he has Wudu, then he realizes that he does not have wudu, he has to repeat the prayer.
Answering your question, the Fatwa Center at Islam Q and A, states:
Tayammum (dry ablution) is prescribed for one who cannot find water, or who can find water but he cannot use it because of illness, or fear of becoming ill.
Based on that, if you did tayammum because there was no water available, then your tayammum was valid, but its validity is temporary and lasts only until the excuse for doing it no longer applies.
When you entered the village, the excuse was no longer applicable, because water was available and it was possible to heat it. So when you prayed Fajr, you did so without being in a state of purity, because you prayed when you were in a state of janaabah (impurity).
Therefore you have to repeat that prayer, but there is no sin on you for that, because you did not deliberately pray in a state of impurity. Allah says: {And there is no blame upon you for that in which you have erred but [only for] what your hearts intended.} (Al-Ahzab 33:5)
Imam An-Nawawi (may Allah have mercy on him) said:
“The Muslims are unanimously agreed that it is forbidden for one who is in a state of impurity to pray, and they are unanimously agreed that such a prayer is not valid, regardless of whether he knew that he was in a state of impurity, or he was unaware of that, or he forgot, but if he prayed out of ignorance or he forgot, there is no sin on him.” (Al-Majmu, 2:67)
Imam Ibn Taymiyah (may Allah have mercy on him) said:
“If someone forgets to purify himself from impurity and prays in that state, then he must repeat the prayer after purifying himself, and there is no difference of scholarly opinion concerning that.” (Majmu al-Fatawa, 22:99)
Almighty Allah knows best.
Source: www.islamqa.info