Just before you spend a lot of money
First, are you relying on the in dash temp gauge? Are you sure it reads correctly? Have you used a different thermometer to check your readings, an infra red or thermocouple driven meter for example.
Second, assuming your temperature is too high, it's not a lot too high. It's worth doing a few things before you bin your radiator.
Feel all over when the engine is good and hot. If the rad is cold everywhere, there is no water getting through. If the hoses to the rad are hot (as you state) there must be some flow, but this might be though the tanks, and not the rad core.
It could be worth running a flushing agent through the system. This may be the same thing as a conditioner that CHAPP refers to.
Then you could remove the radiator and plug all connections except the top most and the bottom most on opposite sides of the core. Stand the rad upright so that the bottom connection is uppermost. Put a hosepipe into the the connection that is now at the top, and see if you get a flow of water from the other open connection. Try reversing the process. If the water comes through OK then your rad is probably OK.
In the UK, some radiator repairers have a rig to test for flow
through the radiator. Perhaps the same is available where you are.
If the rad seems OK, then you may have a problem elsewhere. One or more hoses may have collapsed internally. They may look fine but the inner and outer layers can separate. The water pump impellor may have disintegrated.
Then again, replacing the rad may well solve your problem!