Your model/year of Civic comes with a D17 engine in it. These are known for having head gasket leaks. I had a 2003 (bought it used with 190k miles on it - 2001 through 2005 used the same D17 engine, though some were VTEC and others not). Engine ran great, but sipped coolant. After 2-3 days of driving, it would do exactly what yours is doing with the temps. I can almost guarantee you have a head gasket leak. The problem usually lies in the fact people do not use the Honda blue coolant which is prescribed by Honda. Regular coolant will, over time, eat through the head gasket and start leaking into the cylinder(s). The head gaskets Honda used were very susceptible to this issue.
You might be able to get away with doing a head gasket on it. I found when I took mine apart, the camshaft had some severe wear on it. Replacement of the cam and components alone (cam for it from Honda would have been more than $600US) would have cost more than a JDM engine, which I ended up purchasing. The JDM engine, which they claimed had ~60k miles on it, was ~$550US including tax. I don't know if JDM engines are available in Finland, but it might be something to consider.