The time of Zuhr prayer is when the sun declines (just after mid-day)

Narrated Anas bin Malik:

Allah's Apostle came out as the sun declined at mid-day and offered the Zuhr prayer. He then stood on the pulpit and spoke about the Hour (Day of Judgment) and said that in it there would be tremendous things. He then said, "Whoever likes to ask me about anything he can do so and I shall reply as long as I am at this place of mine. Most of the people wept and the Prophet ﷺ said repeatedly, "Ask me." Abdullah bin Hudhafa As-Sahmi stood up and said, "Who is my father?" The Prophet ﷺ said, "Your father is Hudhafa." The Prophet repeatedly said, "Ask me." Then Umar knelt before him and said, "We are pleased with Allah as our Lord, Islam as our religion, and Muhammad as our Prophet." The Prophet then became quiet and said, "Paradise and Hell-fire were displayed in front of me on this wall just now and I have never seen a better thing (than the former) and a worse thing (than the latter)."

حَدَّثَنَا أَبُو الْيَمَانِ، قَالَ أَخْبَرَنَا شُعَيْبٌ، عَنِ الزُّهْرِيِّ، قَالَ أَخْبَرَنِي أَنَسُ بْنُ مَالِكٍ، أَنَّ رَسُولَ اللَّهِ ﷺ خَرَجَ حِينَ زَاغَتِ الشَّمْسُ فَصَلَّى الظُّهْرَ، فَقَامَ عَلَى الْمِنْبَرِ، فَذَكَرَ السَّاعَةَ، فَذَكَرَ أَنَّ فِيهَا أُمُورًا عِظَامًا ثُمَّ قَالَ " مَنْ أَحَبَّ أَنْ يَسْأَلَ عَنْ شَىْءٍ فَلْيَسْأَلْ، فَلاَ تَسْأَلُونِي عَنْ شَىْءٍ إِلاَّ أَخْبَرْتُكُمْ مَا دُمْتُ فِي مَقَامِي هَذَا ". فَأَكْثَرَ النَّاسُ فِي الْبُكَاءِ، وَأَكْثَرَ أَنْ يَقُولَ " سَلُونِي ". فَقَامَ عَبْدُ اللَّهِ بْنُ حُذَافَةَ السَّهْمِيُّ فَقَالَ مَنْ أَبِي قَالَ " أَبُوكَ حُذَافَةُ ". ثُمَّ أَكْثَرَ أَنْ يَقُولَ " سَلُونِي ". فَبَرَكَ عُمَرُ عَلَى رُكْبَتَيْهِ فَقَالَ رَضِينَا بِاللَّهِ رَبًّا، وَبِالإِسْلاَمِ دِينًا، وَبِمُحَمَّدٍ نَبِيًّا. فَسَكَتَ ثُمَّ قَالَ " عُرِضَتْ عَلَىَّ الْجَنَّةُ وَالنَّارُ آنِفًا فِي عُرْضِ هَذَا الْحَائِطِ فَلَمْ أَرَ كَالْخَيْرِ وَالشَّرِّ ".

Narrated Abu Al-Minhal:

Abu Barza said, "The Prophet used to offer the Fajr (prayer) when one could recognize the person sitting by him (after the prayer) and he used to recite between 60 to 100 Ayat (verses) of the Qur'an. He used to offer the Zuhr prayer as soon as the sun declined (at noon) and the 'Asr at a time when a man might go and return from the farthest place in Medina and find the sun still hot. (The sub-narrator forgot what was said about the Maghrib). He did not mind delaying the 'Isha prayer to one third of the night or the middle of the night."

حَدَّثَنَا حَفْصُ بْنُ عُمَرَ، قَالَ حَدَّثَنَا شُعْبَةُ، عَنْ أَبِي الْمِنْهَالِ، عَنْ أَبِي بَرْزَةَ، كَانَ النَّبِيُّ ﷺ يُصَلِّي الصُّبْحَ وَأَحَدُنَا يَعْرِفُ جَلِيسَهُ، وَيَقْرَأُ فِيهَا مَا بَيْنَ السِّتِّينَ إِلَى الْمِائَةِ، وَيُصَلِّي الظُّهْرَ إِذَا زَالَتِ الشَّمْسُ، وَالْعَصْرَ وَأَحَدُنَا يَذْهَبُ إِلَى أَقْصَى الْمَدِينَةِ ثُمَّ يَرْجِعُ وَالشَّمْسُ حَيَّةٌ، وَنَسِيتُ مَا قَالَ فِي الْمَغْرِبِ، وَلاَ يُبَالِي بِتَأْخِيرِ الْعِشَاءِ إِلَى ثُلُثِ اللَّيْلِ. ثُمَّ قَالَ إِلَى شَطْرِ اللَّيْلِ. وَقَالَ مُعَاذٌ قَالَ شُعْبَةُ ثُمَّ لَقِيتُهُ مَرَّةً فَقَالَ أَوْ ثُلُثِ اللَّيْلِ.