It's theoretically possible for carb heat raise the inlet temp into the carb ice range, but pretty unlikely. Generally, the only downside is a reduction in power.
On the dHC1, warm air (as opposed to hot air) is generally always selected 'on' except at take off. RAF Chippys had it hard-wired to 'warm', with no 'cold' option. But then Brenda's Boys operated from nice long runways!