Do I have to manually find prokaryotic/eukaryotic species from cold/hot habitats and then BLAST my sequence against those? is this the only systematic way?

I don't know of any database that is specific for thermally adapted proteins.  Your approach is correct and probably the best way to make such a  database.

I lifted the following quote for Dalhus et al.., (J. Mol. Biol. (2002) 318, 707–721)

Thermophilic stability arises from a combination of different mechanisms, such as increased number of salt-bridges, hydrogen bonds and aromatic interactions across subunit interfaces..... Further-more, a slight increase in packing density as well as a reduction of the number and volumes of cavities within subunits is observed... 

None of these properties look to be easy to screen for from primary sequence...  However, the structural data in the PDB, is well annotated.  Under the advanced search option I did a text search for: thermophillic and got back 409 PDB entries, for psychrophillic 92 entries, and mesophilic 82 entries... these would be a good place to start.

If you are only looking to make a protein you have be more stable protein... there are several approaches to select for more stable mutants using yeast display libraries.

Hope that helps,

Chris 

To add to what Christopher has said, let's not forget that changing buffer/salt conditions can have a large impact on protein stability as well, since changing pH and salt concentration will affect the number of intramolecular H-bonds (and salt bridges) as opposed to H-bonds between the protein and the bulk solvent. A plot of salt concentration versus protein solubility typically yields a Gaussian curve. If you have a protein that you are working with in PBS pH 7.4 it may be that simply trying another buffer system will improve the thermostability profile enough to carry out whatever assays you are interested in performing.

Our lab routinely uses the thermo-fluor assay to screen for buffer and pH conditions that improve the Tm of our crystallization targets, as well as any additives/ligands that will further improve stability. Hampton sells a pH Slice kit that contains 96 different buffer conditions over a wide pH range. This approach typically yields holding buffers with at least 4-7°C improvements over standard lysis buffers and sometimes can be much greater.