I'm curious, how long would it take for an untreated tooth infection to finally spread to the heart and brain?

Impossible: While this scenario is definitely possible, there is absolutely no way to predict or quantify the risk. Please do not be the test case. If you have an infection get to the doctor to get it treated.

Probably never but: If you already had a bad infection, especially if you were not already on antibiotics, it only takes minutes. To clarify this for you, bacteria from an infection in your jaw could travel in the blood stream to other parts of your body within a minutes. However, that is not to say they would produce a serious problem. Your body's defense mechanisms are always active to defend against such attacks.

Uncertain: There is no real time frame for this for all people. Best to get the infection treated as soon as possible.

Depends: The anatomy of where the infection is will dictated the pace of reaching the brain cavity in particular. While the heart is at some level of risk for a spreading infection systemically, most deaths from infected teeth were attributable to brain infections.