Much of the HOT information I have read about this topic originates from Transport Canada and FAA winter operations guidelines. I think it’s important to remember this is all to assist the judgement of the Captain. HOT is not a limitation, just a guide. Based on elapsed time and conditions a take-off may be permitted following an inspection. There are different types of inspections!
I would suggest some time searching FAA and TC websites with some background information regarding HOT tables if your Airlines doesn’t provide it. The tables alone are only a small part of the story!