Who came up with the idea of placing the President pro tempore of the Senate 3rd in the line of succession anyway? Sounds to me like a immensely stupid idea to elevate a senile fossil to the presidency in the case the President, the Vice President, and the Speaker of the House have all died/resigned/were impeached. 
Why not go on with the Secretary of State after the Speaker of the House?
The role provided in the Constitution for the Vice President, is as President of the Senate, and secondarily as successor to the President. The President pro tempore, became the presiding officer over the Senate when the vice president was absent or the vice presidency was vacant (as it often was, either due to death of the President or Vice President). Until 1890, the post literally was a temporary assignment, while the VP was gone.
The original succession law provided that the President pro tempore would become acting President in case of a double vacancy. This was logical given that the he was the backup president of the Senate, behind the Vice President. The original succession law also provided for a special election of president in case of a double vacancy. The President pro tempore would only act as President until the election was held.
In 1886, both the House Speaker and Senate President pro tempore were removed from the succession, and the cabinet substituted, and in 1890 the Senate President pro tempore was made a permanent position (until a new person was chosen).
The succession order was changed in 1947, to reinsert the House Speaker and the President pro tempore, but the order was reversed. This was done in part because Truman did not think that it was a good idea for Secretary of State Stettinius, who had never run for elective office to become President.
It was also around this time that the custom became for the longest serving member of the majority party to be President pro tempore. In part this was due to the development of the positions of Senate majority and minority leader who control the actual business of the Senate.
In 1953, Richard Nixon became the first VP to have his office at the White House, rather than the Capitol, and has led us to think of the VP as part of the executive, rather than the legislature.
In Texas, the Lieutenant Governor is very much in reality the presiding officer of the Senate. The Texas Constitution also provides for the Senate President Pro Tempore to become the acting Lieutenant Governor. Under other provisions of the constitution making the Lieutenant Governor the acting governor, the President Pro Tempore is 2nd in line for succession. The succession beyond that is set by law. The Constitution also provides for election of a new Lieutenant Governor by the Senate, which was first used when Governor Bush resigned to become President of the United States, and the Lieutenant Governor, Rick Perry, became Governor.
A curiousity in Texas, is that if the Governor and Lieutenant Governor are out of the state, then the President Pro Tempore is the acting governor. A tradition has been established by which a long-serving senator is elected President Pro Tempore, and then has a day when they are Governor for a Day.
