My baby was born five days ago, and we’ve just returned home. I need to ensure he is dressed appropriately for the hot weather, both day and night. I've noticed that he occasionally gets very warm and red during the day, despite feeding him and using a fan to cool the room. Could you please recommend how to dress him safely during the day and night?

There is no perfect bedding/clothing amount recommended for baby when sleeping.
Red Nose recommends dressing baby according to the room temperature. Babies do not need large amounts of bedding/clothing but similar to what you as a parent would wear in the same environment.

Red Nose has the following information on our web site about bedding amount & overheating.
Have a look & let me know if you have any further questions.

https://rednose.org.au/article/how-much-bedding-does-baby-need  **
https://rednose.org.au/article/protecting-baby-from-overheating-during-sleep  **

https://rednose.org.au/article/what-is-a-safe-room-temperature-for-sleeping-baby
https://rednose.org.au/article/how-to-dress-baby-for-sleep

Is sounds like he may have had too much bedding if he felt very warm & was red in face.
Ensure his head (& face) are not covered when sleeping. Wearing of hats/bonnets are not recommended when baby is sleeping.
A fan can be helpful, particularly on these very hot days.

Have you had your follow up visits with your Midwife &/or Maternal/Child Health Nurse?
They are also a good resource for these types of questions.
Remember, baby may require extra liquid (eg breastfeeding) during hot weather.