TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Group: The thermal cross-linking group is chosen from group of formulae (3-8). Content of thermal cross-linking group in the polymer molecule is 0.000001-0.001 mol/g.R1-R9=H, 1-10C alkyl, phenyl, 6-20C aromatic group or halogen;A=H, 1-10C hydrocarbon, halogen, nitro or -SO3Y group;Y=H or monovalent cation;andm=1-4.    TECHNOLOGY FOCUS - POLYMERS - Preferred Polymer: The sulfonic acid group-containing heat-cross-linkable polymer further has dibenzyl group-containing structures of formulae (13,14).X,Y=same as defined above;Z5,Z6=O or S;andAr2=bivalent aromatic group chosen from group of formula (9-12), preferably group of formula (12).Preferred Composition: The polymer satisfies relations: 0.9less than or equal to (n3+n4+n5+n6)/(n3+n4+n5+n6+n7)less than or equal to 1, 0.05less than or equal to (n3+n4)/(n3+n4+n5+n6)less than or equal to 0.7, 0.01less than or equal to (n4+n6)/(n3+n4+n5+n6)less than or equal to 0.95, where n3 is mol% of structure (13), n4 is mol% of structure (1), n5 is mol% of structure (14), n6 is mol% of structure (2) and n7 is mol% of other repeating structure. A sulfonic acid group-containing heat-cross-linkable polymer composition is formed by carrying out heat-bridge of at least a portion of thermal-cross-linking group of sulfonic acid group-containing heat-cross-linkable polymer (1-100 wt.%). Preferred Definitions:    Ar1=group of formula (9-12), preferably group of formula (12);    Z1-Z4=O or S, preferably O;and    n1,n2=3 or more, preferably 1.    EXAMPLE - 3,3'-disulfonic-acid sodium-4,4'-dichloro diphenyl sulfone (in g) (31.212), 2,6-dichlorobenzonitrile (18.609), SPECIANOL-DPE-PL (RTM: terminal hydroxyl group-containing phenylene ether oligomer of formula (23)) (94.11), potassium carbonate (26.107) and N-methyl-2-pyrrolidone (420) were heat-stirred at 190-200degrees C for 12 hours, and reacted at 140degrees C for 3 hours. 4-ethynyl phenol (0.41) was added and stirred, after cooling the reaction solution. The reaction solution was poured into water, and strand-shaped polymer was settled. The settled polymer was cleaned with water at room temperature, and dried to obtain a polymer having thermal cross-linking group. The obtained polymer (8) was dissolved in dimethyl acetamide (32) to obtain a solution. The obtained solution was applied on glass plate by thickness of 200 microns, and dried under reduced pressure for 3 days at 70degrees C. The obtained film was removed from the plate, and immersed into sulfuric acid for 1 hour. The sulfonic acid group of the polymer was converted into acidic group, and polymer electrolyte membrane was obtained. The obtained polymer electrolyte membrane had excellent swelling-proof property, workability and high proton conductivity.    n=5.