Can you blow your engine if the temperarure of the engine is low or normal?

Absolutely. The head gaskets on my Subaru blew when the engine had been running for only five minutes. "Blowing" is kind of a woolly term, though, so you may need to be more specific.

"Blowing" your engine can be done in many ways, irrespective of temperatures.

You can blow your engine at any temperature. I'm not sure what the context of your question is.

Put it in neutral and floor it. It will blow in a minute or three and the engine temperature will be low or normal.

Sure it happens all the time because people never learn that changing the oil and filter needs to be done every 3,000 miles. Now that car manufacturers have put the electronic oil change reminders in vehicles people are mislead into believing everything will be fine if following a 7,500 mile oil change schedule. The motor will make it past the warranty period 10,000 miles and then you need a new motor because of bearing failure. If the oil gets black or if you let the oil level drop so it doesn't register on the dipstick you'll ruin the motor.

Yes if you crash your car and seriously damage your engine at a low temperature.