hot ‧ ly /ˈhɒtli $ ˈhɑːtli/ BrE AmE adverb
1 . in an excited or angry way
hotly debated/disputed/denied etc
The rumor has been hotly denied.
2 . done with a lot of energy and effort:
one of the most hotly contested congressional elections
The man ran out of the store, hotly pursued (=chased closely) by security guards.