All
batteries will warm a little, especially during the bulk stage of the charge cycle.
On many Li-ion battery chargers the red light is constantly lit for most of the charge cycle. As the battery approaches full charge the green and red lights will flash alternately: faster at first, slower as time passes. When the battery is fully charged the green light will stay lit constantly and the red light will not light. Better quality chargers will shut down charging completely when full charge is reached (usually just below 4.2V), others may leave the battery on a trickle charge. Best to remove
batteries as soon as possible after the solid green light shows, unless you know for sure the charger will shut down after full charge is achieved.
Don't know if this is how the Provari charging lights operate, though. I'm sure another Provari owner will drop by.