performing obligatory Salahs at the start of their prescribed times is Mustahab (desirable), but at times of severe heat, you will be permitted to delay Zhuhr (Noon) prayer until the weather becomes cooler provided that you perform it before 'Asr (afternoon) Prayer. Consequently, you will be permitted to delay performing Zhuhr (Noon) prayer provided that you perform it before the end of its due time and before the time of 'Asr (Afternoon) prayer is due.
performing Salah without making Wudu' or with washing some of the obligatory parts of Wudu' is prohibited and a great sin. Doing so renders the Salah invalid. Whoever does so should make up for that Salah again. (Part No. 6; Page No. 117) May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.