What is the hottest star that we know of and how hotter is it than the sun?

The hottest stars are those that appear bluish, such as Sirius.

Cygnus OB2-12 is a very bright blue hypergiant that lies between 5,000-6,000 light-years from Earth. It is with an absolute magnitude of -12.2. It is more than 6 million times brighter than the Sun, and among the most luminous stars known in the Galaxy.

The hottest star visible to the naked eye is Theta Orionis C, one of the stars illuminating the Orion nebula. It has a surface temperature of about 45,000 K.

Even hotter is a star going by the rather unmemorable name of HD 93129A; which is about 7,500 light-years away. Its surface temperature is around 50,000 K. However, it's quite distant and thus can't be seen without a telescope.

Over a short period of time, the Neutron Star burns at a temperature of over 1 billion degrees kelvin. However, the huge number of neutrinos it emits carries away so much energy that the temperature falls within a few years to around 1 million kelvins.

For comparison, the Sun's surface temperature is about 6000 K.

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Blue hypergiant stars like Eta Carinae.

The Sun's temperature is 6,000 K

Eta Carinae is 36,000-40,000 Kelvin

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The hottest stars are (big and) blue to our eye.

Eta Carinae (orion) could be as large as 180 times the radius of the Sun, and its surface temperature is 36,000-40,000 Kelvin.

40,000 Kelvin is 72,000 degrees F.