Starting at the beginning what do you call "affordable"? My idea of affordable and your idea of affordable might just not quite be the same.
It sounds like what you want is commonly called a surface temperature probe which are probes designed with a tip for measuring a surface temperature. Google surface Temperature Probes to get some ideas. I saw several through Amazon that run around $40.00 USD each. That brings us to how many points do you want to measure? Do you just want a single probe that you move from point to point or do you want to use multiple probes all collecting data at the same time?
There is a number of ways to get the temperature data into a computer the question is once we feed the data to the computer what do you want to do with it? There are dozens of small simple data acquisition systems out there that can get the data to a PC and chart it by channel. This will always go back to budget?
Here are a few images of something I did years ago to monitor and compare case temperatures in a server type computer. The thermocouples could have easily been measuring surface temperatures and easily been recorded and charted.
A quick and simple turn key system could be made from
one of these which would give you four thermocouple channels and the basic charting software. If you better explain exactly in detail what you want to do I am sure there is a solution.
Ron