Is the blue giant star the hottest star?
Yes, Blue giant stars are the hottest class of stars.
(for previous the answerers information, betelgeuse is a RED supergiant)
If you mean "What is the hottest star". The hottest stars are the blue stars. A star appears blue once its surface temperature gets above 10,000 Kelvin, or so, a star will appear blue to our eyes. So the hottest stars in the Universe are going to be a blue star, and we know they're going to be massive.
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A stars color is determined mainly by it's surface temperature. They tend to range from Blue (hottest) thru white and yellow to red (coolest). One thing to bear in mind tho is that a Red Giant star, for example, produces more heat than a smaller yellow star but because the star is much bigger the heat is more spread out (because the surface area is so much bigger) and therefore it appears red.