Hot sauce rarely goes bad and can last for years unopened or just out at room temperature.
Hot sauce does not require any refrigeration but you can keep the hot sauce fresher longer by refrigerating it.
Still if you happen to eat bad or soured hot sauce the worse thing that would happen is you get a stomach ache, diarrhea, vomiting etc.
It's unlikely to cause any serious health issues and you'd likely stop eating the hot sauce that is bad well before you consumed enough of it to cause any health issues.
If the hot sauce smells bad or has any mold in it then throw it out.
And if you taste the hot sauce and it tastes bad throw it out to avoid making yourself sick.