I have been told by some people that the HD sets get very hot and overheat with frequent problems. Hope this is not true as I purchased one recently.
Any opinions?

Overheating used to be an issue, but without knowing the brand and your location it's difficult to comment further.

Would overheating be a problem for an LED HD set located in the State of Florida?
It's an LG Brand.
Thanks.

As long as there is air flow around the set you will be fine.