Thamud nation is an example of the one who deceives himself, desires the fatal and does not follow Allah’s commands nor His prophet’s (saws).
Allah (swt) guided them to the way of righteousness, benevolent, purity and the goodness, but they preferred disbelieving, as Allah (swt) said:
{وَأَمَّا ثَمُودُ فَهَدَيْنَاهُمْ فَاسْتَحَبُّوا الْعَمَىٰ عَلَى الْهُدَىٰ فَأَخَذَتْهُمْ صَاعِقَةُ الْعَذَابِ الْهُونِ بِمَا كَانُوا يَكْسِبُونَ}
(And as for Thamud, We guided them, but they preferred blindness over guidance, so the thunderbolt of humiliating punishment seized them for what they used to earn.) (Fussilat: 17)
The calling of the Prophet Saleh (pbuh) to his people was as all the other callings of the Prophets (pbut). Allah (swt) said:
{وَإِلَىٰ ثَمُودَ أَخَاهُمْ صَالِحًا ۗ قَالَ يَا قَوْمِ اعْبُدُوا اللَّهَ مَا لَكُم مِّنْ إِلَٰهٍ غَيْرُهُ}
(And to the Thamud [We sent] their brother Salih. He said, “O my people, worship Allah; you have no deity other than Him.) (Al-A’raaf: 73)
The miracle which they asked for to testify to his true calling from Allah (swt) was a camel with a child in her belly. Allah (swt), then, brought it to them out of a certain rock which they specified. Saleh (pbuh) said to them, as stated in the Holy Quran:
{قَدْ جَاءَتْكُم بَيِّنَةٌ مِّن رَّبِّكُمْ ۖ هَٰذِهِ نَاقَةُ اللَّهِ لَكُمْ آيَةً ۖ فَذَرُوهَا تَأْكُلْ فِي أَرْضِ اللَّهِ ۖ وَلَا تَمَسُّوهَا بِسُوءٍ فَيَأْخُذَكُمْ عَذَابٌ أَلِيمٌ }
(There has come to you clear evidence from your Lord. This is the she-camel of Allah [sent] to you as a sign. So leave her to eat within Allah ‘s land and do not touch her with harm, lest there seize you a painful punishment.) (Al-A’raaf: 73)
Allah (swt) has made it beneficial to Thamoud’s people; it produced milk that has never been known before, in return it drinks one day from the well and the people drink the next day. Allah (swt) said:
{قَالَ هَٰذِهِ نَاقَةٌ لَّهَا شِرْبٌ وَلَكُمْ شِرْبُ يَوْمٍ مَّعْلُومٍ }
(He said, “This is a she-camel. For her is a [time of] drink, and for you is a [time of] drink, [each] on a known day.) (Ash-Shu’araa: 155)
By this way they got water and milk, but they disbelieved in Allah (swt) and His blessings and in Saleh (pbuh), that is why Allah (swt) says:
{كَذَّبَتْ ثَمُودُ بِطَغْوَاهَا}
(Thamud denied [their prophet] by reason of their transgression, (11))
Thamud denied, so did peoples of Aad, Lott, Shaua’ib, Noah and Ibrahim (pbut), even the people of the Prophet Muhammad (saws). Allah (swt) says:
{إِن يُكَذِّبُوكَ فَقَدْ كَذَّبَتْ قَبْلَهُمْ قَوْمُ نُوحٍ وَعَادٌ وَثَمُودُ % وَقَوْمُ إِبْرَاهِيمَ وَقَوْمُ لُوطٍ % وَأَصْحَابُ مَدْيَنَ ۖ وَكُذِّبَ مُوسَىٰ فَأَمْلَيْتُ لِلْكَافِرِينَ ثُمَّ أَخَذْتُهُمْ ۖ فَكَيْفَ كَانَ نَكِيرِ }
(And if they deny you, [O Muhammad] – so, before them, did the people of Noah and ‘Aad and Thamud deny [their prophets], % And the people of Abraham and the people of Lot % And the inhabitants of Madyan. And Moses was denied, so I prolonged enjoyment for the disbelievers; then I seized them, and how [terrible] was My reproach.) (Al-Hajj: 42-44)
Thamud transgressed and exceeded all the limits, as they did not only deny the Prophet, but they killed the camel that used to give people milk, hence, their transgression was the ultimate sin, that is what some scholars said, among them is Mujahed: Their transgression refers to their sin.
It is also said that (their transgression) means (their punishment) which Saleh (pbuh) has promised them, so this punishment was overpowered them, as Allah (swt) said:
{ فَأَمَّا ثَمُودُ فَأُهْلِكُوا بِالطَّاغِيَةِ }
(So as for Thamud, they were destroyed by the overpowering [blast].) (Al-Haaqqa: 5)