I would like to check in which constellation the Sun was in at some time in the past, any recommendations how to do that?
There are plenty of online planetarium sites which should be able to do this for you. This one is the first hit for a Google search for "online planetarium software"
- If you're talking about short time periods and don't need a lot of detail, a lookup table such as this one: http://spaceplace.nasa.gov/starfinder3/en/ will work just fine.
- For more detail, you'll have to calculate the position of the Sun on the background stars and determine that moment when the position crosses the (somewhat arbitrarily defined) constellation boundaries. Wikipedia has good introductory equations to determine the Sun's position (https://en.wikipedia.org/wiki/Position_of_the_Sun) though David Colarusso's site has much more information: http://www.davidcolarusso.com/astro/. There are other equations you can use to determine which side of the line the Sun's position lies: https://stackoverflow.com/questions/1560492/how-to-tell-whether-a-point-is-to-the-right-or-left-side-of-a-line.
- For long time periods, you'll have to do what's in the previous point and also determine how the Earth's position changes in relation to the Sun and where in the galaxy the Sun lies. I'll leave that as an exercise for you since I'm not sure you want that level of detail.
In this case, Wolfram|Alpha has you covered. For example, look at the result for "which constellation was the Sun in Jan 1 1400". That said, I'm not sure this calculate includes the precession of the Earth's rotation axis, since I would've expected it to get my astrological birth sign right in 500 BC.