I can't remember which engine manufacturer it was, but I read in a technical document by them that all their carburettor based engines could be subject to icing at up to 32C.
Don't forget that warmer air can hold more water, so on a warm day carb ice can build faster than a cold day. I read an AAIB report about a Jabiru which flew through the cloud from a cooling tower at a power station. This was very warm but very humid air. Even with full carb heat it still crashed.
Carb heat has to be able to raise the carb air temp by 50C. This suggests that the carb ice temperature range is pretty broad.
I've got some graphs if you'd like to see them.