[scientist@work (OP)]

Is there any attempt to measure the distance to the sun?
It can't be that far because we can feel the heat on the earth, still.
Imagine the heat it has up there, unbelivable.

[Kryptid]

It's about 93 million miles (150 million kilometers) from Earth on average. It releases a lot of radiation, which is why we can still feel its heat at such a great distance.

[Janus]

Put in other terms:
You could fit about 30 Earth's between the Earth and the Moon, and the Sun is 400 times further away than that.
At this distance, the Earth only intercepts 0.000000045% of the light and heat put out by the Sun, and even that small fraction is 173,000,000,000,000,000, watts or 100,000 times the total world energy usage.

That being said, the surface of the Sun is  just ~5,500̊ C or a bit shy of 10,000̊ F

[Bored chemist]

Is there any attempt to measure the distance to the sun?

Yes, repeatedly over the last 2500 years or so.
https://en.wikipedia.org/wiki/Astronomical_unit#History