I was taught that the crew in the boat let the furnace get too hot leading to an explosion in the ship which caused it to sink. My history teacher taught me this and explained a story where they sent people to go look at the remains and they almost were positive that the ship was not sunk by german u-boats. I went online to search this up and I can't find anything about that. Was I taught wrong or is there actually evidence to back this up?
There is actually a some truth to the suggestion that the steam system of the Lusitania led to the sinking. However, that is only after a torpedo from the German U boat U-20 exploded against the hull of ship. So you were taught wrong.
The initial problem is that the torpedoes used by the U-20 were only capable of punching a 20 feet diameter hole in the side of a ship. Initial accounts say that one confirmed, or possibly two torpedoes struck the ship. With a ~ 1,000 foot long ship, it's hard to explain how it sank in less than 20 minutes. The Titanic took much longer to sink with far more damage.
The Lusitania, like other contemporary liners, used multiple boilers to make enough steam to power the engines that propelled the ship. The steam was collected by a network of pipes that led to the engine rooms. This network of pipes was pressurized at several hundred pounds per square inch and proved to be the vulnerable failure point in the ship. The suggestion is that by sheer bad luck, the torpedo struck the Lusitania just in the spot that the steam piping would be vulnerable to the minor flooding that a 20 foot diameter hole would cause.
I suggest you read Lusitania - An Epic Tragedy by Diana Preston. That is the reference I am using for this reply.