High carbon, stainless, and fancy stuff is where you can run into problems. In general you won't see this on car or bike frames, too expensive in bulk.
If it's a newer bike it's probably aluminum which you can usually still weld with impunity. If it was high grade alloy the heat could matter, but as far as I know nobody cares that much about bike frames. Heat treatment, or "seasoning" in the case of some aluminum is expensive.
Source: used to cut up old bikes and weld the frames into crazy chariot contraptions we would tow around
Steel is real, man. It'll bend, not break.
But in seriousness, yeah, I was following very closely behind a fellow who snapped his fork jumping over a bump in the road. I almost went over him. Despite the helmet, he lost memory of the accident. I called an ambulance for him and left my number. He called me the next day asking what had happened.
It was a nice aluminum frame, looked in good condition. Always check carefully for hairline fractures when buying a used aluminum bike.
Drilling for rivets is also dangerous when done incorrectly. You do not want to be riding at full steam when the frame cracks, it's nasty.