Why it feels hotter at Night?

Regarding the outside temperatures check the humidity levels outside. The most likely reason it feels hotter at night is the humidity might be higher than during the day.

Concerning the inside of the house being hotter at night than outside, that is mostly likely due to house accumulating heating during day and everything inside, furniture, walls, etc. is hot at the end of the day. Outside may be cooler because the sun has gone down and there may be a change of wind/breeze. Inside the inside the house, everyhting needs to loose heat via radiation before the air feels cooler.

During the day, the sunlight is kept out of your house by the roof (assuming you don't have a glass ceiling or windows on your roof). At night, the sun sets and the outside atmosphere is allowed to emit infrared radiation. If there are clouds out, they emit infrared radiation back down to the surface. The atmosphere, itself, also emits radiation back (greenhouse effect), so the surface doesn't get too cold.

Now let's compare what happens at night in your house. Presumably, your roof and house absorbs a lot of radiation during the day. During the night, your house emits radiation, but more than outside, since it is hotter (Stefan-Boltzmann equation). Your roof/ceiling emits radiation both inside and outside the house. This keeps the radiation "trapped" inside the house.