After soldering all the components onto the Humble Pi (magnificent add-on board!), I am now able to put the project onto my RasPi without having to be careful about the jumper cables.
I've also got rid of LCD screen resistors, as they are not that needed and put 4.7k Î© resistor instead of the 10k Î© for the temperature sensor. The temperature sensor doesn't need that much resistance, but the 4.7k Î© is the minimum. The readings did not change at all. That's good, I know it works well (or, does it?).
The code changed a bit as well, I've created a "boot" screen and moved time/date onto a separate screen. Now the LCD Monitor has a default 10 second display time for time/date and temperature. Looks good, works fine. I've tested it and let it running for a full day. No delays, lags, problems, the RPi didn't heat up.
The only thing I had to do to get more precise temperature readings was to put the sensor further from the Pi. It's heat mingled with temperature readings and gave unreasonable readings.
Now, I can start doing more with the project. I've already ordered humidity sensor and am starting to write code for button inputs to make it more usable.
If you're interested in the python code for this project, head on to my github repository: LCD-Monitor.