Don't use a thermocouple. They have a very small output and the reading depends on the temperature of the cold junction.
Better would be a RTD, which is a resistance that changes with temperature.
However, I would recommend a temperature sensing IC, such as an LM73
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If you want to have fewer wires and you don't mind a slightly worse resolution, you could use one of the Maxim 1-wire range, such as the DS1825
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These ICs measure temperature directly, and so there is no other data conversion to do. They interface directly to microcontrollers.
If you use a microcontroller such as the 16F876, there is an I2C port for connecting to the LM73, and a serial port that connects to a computer. You can use a smaller microcontroller like a 12F629 but the code to connect to the temperature sensor and the PC is a bit more complicated. This is because the 12F629 doesn't have the specialised ports, so the routines have to programmed in code.
I don't think that there are any microcontrollers that have ports specifically for connecting to the 1-wire sensors, so the interface to them has to be programmed in code for all microcontrollers.
The voltage levels that a serial port on a computer works at is bigger than microcontrollers work at, so a converter such as a MAX232 or similar is needed.
To log the data, you could quite easily program a microcontroller to read the temperature and output it on a serial line to the serial port on a computer. On the computer, there are lots of terminal emulator programs that can record to a file what arrives on a serial port.
The overall scheme is:-
LM73 converts temperature to serial data
PIC initiates reading the temperature and outputs data in a different format
MAX232 converts the voltage level to RS232 levels
Terminal emulator program. Reads the serial port and stores the data to a file.