Whether or not the core is hotter than the corona depends on what type of "hotter" you are looking for.
If we examine our own sun, then we see that on average the core is about 15 million degrees Celsius while the Corona is only 1 to 2 million degrees. However, there are occasionally highly active parts of the corona called solar flares where temperatures can go above 20 million degrees Celsius.
What solar flares are and why they happen is still somewhat of a mystery, and scientists are still observing and looking for ways to explain them. Also, solar flares aren't the only mystery that the corona has for science. Scientists believe the core of the star must be 15 million degrees Celsius because such high temperatures are necessary for fusion when light nuclei like hydrogen are smashed so hard together they fuse and release energy. The temperature goes down as one goes from the core to the surface of the sun, but past the surface lies the corona, and in the corona the temperature increases rather than decreases with increasing distance from the sun! Why the corona has these interesting characteristics is an area of active research.
So the answer to your question is most of the time the core is hotter than the corona, but there are powerful events called solar flares, which science is still trying to understand, that can beat out even the core. I hope this answer further sparks your curiosity and helps you see that science is still growing in order to better explain nature. Keep up the good questions!

The corona is definitely hotter than the Earth's core but it is cooler than the Sun's core. I looked up some numbers for you. The temperature of the corona is about 1,000,000 degrees Celsius and the temperature of the sun's core is about 15,000,000 degrees Celsius. In contrast, the temperature of the Earth's core is about 3,000-5,000 degrees Celsius.

Yes, the core of the sun is hotter than the corona. The core is something like 15 million degrees C, and the corona is at something like 2 to 4 million degrees. The corona is hotter than the surface of the sun, but not as hot as the core (where thermonuclear fusion reactions are taking place,which keep the sun "alive").