I live in a city that is not relatively large but what surprises me is that I find two different times for the prayer of Thuhr and two Athaans as well. What is the ruling on this?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

There is no harm in having multiple mosques in a city. If this is the case, then there is no harm if some mosques perform prayer early while others delay it as long as this is done within the preferred time. Jibreel (i.e. Gabriel) prayed the Thuhr prayer with the Prophet, sallallaahu ‘alayhi wa sallam, one day when the sun had passed its zenith. On the following day he prayed it with him when the shadow of anything was equivalent to it in length and said: “The time (for prayer) is between these two times.” [Al-Mustadrak, An-Nasaa’i, Abu Daawood, At-Tirmithi; Al-Albaani and Al-Arna’oot: Saheeh]

Imaam Muslim reported in his Saheeh, from Abu Moosa that a man came to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, asking him about the times of prayer and he did not answer him. The Iqaamah for Fajr was then called at the break of dawn while (it was so dark that) the people were not able to recognize each other. Then, he commanded that the Iqaamah be called for Thuhr when the sun had passed its zenith. The following day he delayed the Thuhr prayer until it was nearly the time of ‘Asr. He then said: “The time (for prayer) is between these two (times).”

The Prophet, sallallaahu ‘alayhi wa sallam, would delay the Thuhr prayer in case of intense heat and would order others to do the same.

Anas narrated that the Prophet, sallallaahu ‘alayhi wa sallam, would offer the prayer earlier if it was very cold and, if it was very hot, he would delay it.” [Al-Bukhari]

Abu Tharr narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: “If it is intensely hot, wait until it cools down before you pray, for intense heat is from the fumes of the Hellfire.” [Al-Bukhari and Muslim] 

Ibn Hajar mentioned the different opinions of scholars regarding the reason behind waiting until it cools down in Fat-h Al-Baari, saying: “Until a shadow the length of a cubit (i.e. an arm) after when the sun passed its zenith.” It was also said: “(When the shadow is) a quarter of the stature (it represents).”

Accordingly, the matter is broad in scope. So a Muslim should think the best of the people of the mosque and be keen on observing prayer with them, keeping them united and not provoking disagreements among them, due to the questions that arise from the broad scope of the evidence involved.