Corrections in red.  Stylistics in blue.

A Day Without Electricity.

Today was a terrible day. At 12:30 p.m. there was a power outage, which ended at 10:05 p.m. It is often hot in my city (the feels like temperature was around 40 degrees Celsius), and we needed air conditioning.  But without electricity there wasn't any air conditioning. At 7:00 p.m. I wanted to die. I was angry, tired, and hungry.

When using the 24-hour clock, you don't need a.m. or p.m.  So I changed the 24-hour clock to the 12-hour clock.  Alternatively, you could say:  "At 12:30 there was..... ended at 22:05."

A Day Without Electricity

Today was a terrible day. At 12:30 p.m. there was a power outage, lasting until 22:05 p.m. My city is very hot and with the RealFeel temperature hovering around 40 degrees Celsius, air conditioning is absolutely essential. Of course, without electricity, there can be no air conditioning. At 7:00 p.m, I wanted to die. I was angry, tired and hungry.

Nice job, Andrea!

Here are a few different ways I would construct this sentence

In my city there are a hot weather (the real feel temperature was around 40 degrees celsius) and we need an air condition, without electricity there wasn't air condition.

The weather in my city is hot (the temperature outside felt like 40C). We need air conditioning, but without power it was impossible. 

It gets hot in my city. The real feel temperature was up to 40 degrees centigrade. We need air conditioning! Unfortunately, with no power there is no AC.

<em>Here's how a frustrated American might say it</em>

It's damn hot outside man.  Weatherman says it feels like 40 out here.  We sure need some air conditioning but since there isn't any power we cant turn it on. 

A day without electricity.

Today was a terrible day. At 12:30 p.m. there was a power outage, and it finished at 22:05 p.m. In my city the weather is hot (the temperature actually feels like 40 degrees celsius), and we need air conditioning. Without electricity, there is no air conditionin. At 7:00 p.m. I wanted to die. I was angry, tired and hungry.

A day without electricity.

Today was a terrible day! At 12:30 p.m. there was a power outage, that lasted all the way till 10:05 p.m. It's quite hot in my city (the temperature was around 40 degrees celsius) and so we really need air-conditioners. And without electricity, the air-conditioners don't work. By 7:00 p.m, I wanted to die! I was angry, tired and hungry!