Letter To A Manager

Dear Sir,
I am writing to explain to you* about a problem which that I faced when I stayed while staying in a Four Season hotel.

Last week I visited London for three days to give a speech on the at an important conference. Before visiting the city I had decided to choose your hotel**, because your website advertised you as the best hostel in the city with convinient facilities and friendly staff.
On the third day in London the weather was extremely hot and outside temperature rised rose until to 30 degrees Celsiums. In my room the temperature was quite high too because the cooling system didn't wasn't working properly. It suddenly stopped, and after some time started working again. It was awful because I got caught a cough due to the cooling system which after it started working again at night when while I was sleeping.
I'd like to ask you for a discount for next time as I am planning to stay in your hotel soon.
I am looking forward for to your response.

Yours faithfully,
Sergey I.

* The verb to explain needs to be directed with a "to". It's the same as the verb "to say", e.g. I will say to you ...

** This is correct as it is, but usually it wouldn't be said like you have said it, perhaps "Before visiting the city I chose your hotel because .." or "... I booked with your hotel because .." instead.

Saying that you've decided to choose a hotel makes it sound like the hotel hasn't been booked yet. That's possible in the future tense but awkward in the past. In the past tense it could be used like "I decided to choose hotel zzz but there were no rooms available so I had to stay somewhere else instead"