"It's half as hot as the sun"

I Haven't seen Blade: Trinity yet, but this depends on what they mean with the temperature of the sun. In the core of the sun the temperature is many millions of degrees and in the corona (gases surrounding the sun) the temperature can also be several million degrees Kelvin. However, the surface temperature of the Sun is 'only' about 5700 Kelvin. This would mean the weapon has a temperature of 2850 Kelvin (2577 degrees Celsius, 4671 degrees Fahrenheit). This is very hot, but certainly not impossible. Acetylene/oxygen flames used for welding can reach temperatures of more than 6000 degrees Fahrenheit. Thermite can also provide temperatures of more than 4000 degrees Fahrenheit.

Also this doesn't mean that were talking about the same amount of energy as the sun. The sun is so big that the amount of energy we're talking about is ridiculous. However it is possible to make very small parts very hot (a lot hotter than the Sun). The record temperature reached in a lab is an almost unbelievable 5.5 trillion degrees Celsius in the Large Hadron Collider (more than 250 thousand times hotter than the core of the Sun). However, the amount of mass at this temperature is miniscule as is the time they stay at this temperature. Therefore it would be (at least with current technology) impossible to make a weapon with these kind of temperatures.

So if we're talking about surface temperatures of the Sun (photosphere) this would certainly be possible without nuclear power and without widespread destruction. With current technology, this wouldn't be possible if we're talking about core or corona temperatures.