I agree, don't take the thermostat internals out. The car is designed to work in climates like Spain, its not even particularly warm there compared to some places the punto was sold. As stated before, I don't even think its overheating anyway but if it does it then its indicating something is wrong, masking said issue by removing stat internals is never the answer. I don't even think the OP really has an issue here, 75-80 rising to 90 is totally fine, 90 is a bit high for moving along and not in town.
Really if you are worried about it then you just need to give the cooling system a once over. In no particular order....
-when was the coolant last change, what does it look like - clena or all mucky and brown? If dirty then it needs draining and properly flushing through to clean it (not just drain and refill! drain, fill with water and flush, run for a bit, drain and fill with clean water, run upto temp and drain, repeat until only clean water comes out and then fill with coolant and water) and refilling with proper 50/50 coolant water mix.
-check thermostat operation, to test it you need to take it off really and at this point they are so cheap you may as well just stick a new one on and be done, crucial part fo the system so recommend genuine and not cheapy one off ebay etc. (perfect opportunity to flush the system)
-check rad fan operates properly, comes on at the right temp etc - if not change the thermo-switch on the side, check and clean connections at same time
-check the condition of the rad fan itself, does it turn nice and freely by hand or not? If not replace.
-check the condition of the rad itself, are the fins all damaged and/or corroded - if so replace. Run water through it (in reverse to normal operation), does it seem to be clear and not blocked? If blocked going backwards may flush it out, if not replace.
-Is the system properly bled, see guides section
-Probably the last thing to look at is replacing the waterpump - but really if it needs replacing it will be noisy rather than just not pumping. So generally advise this is just changed when the timing belt is renewed as its not expensive and its basicaly a few bolts if you have the belts off.
A mk1 Punto is not a new car anymore so its really probable if one of or some of the components of the cooling system could do with being replaced - of course they might not be original but if you don't have history to prove something has been done you must assume its never been done.
