Tom if you have not done so already have a look at the Ardunio.
It would seem to do the stuff you want to do. The basics don't need an external programmer and there is a big online community. There are other versions, some simpler and cheaper and I may eventually use one of them for the actual build and use the Duemilanove for learning and experimenting. A lot of work also seems to be happening with PIC's but
I've not worked out just what is needed to get going with them.
The broad specs of the Duemilanove are as follows
http://arduino.cc/en/Main/ArduinoBoardDuemilanove
Summary
Microcontroller ATmega168 (mines a 328)
Operating Voltage 5V
Input Voltage (recommended) 7-12V
Input Voltage (limits) 6-20V
Digital I/O Pins 14 (of which 6 provide PWM output)
Analog Input Pins 6
DC Current per I/O Pin 40 mA
DC Current for 3.3V Pin 50 mA
Flash Memory 16 KB (ATmega168) or 32 KB (ATmega328) of which 2 KB used by bootloader
SRAM 1 KB (ATmega168) or 2 KB (ATmega328)
EEPROM 512 bytes (ATmega168) or 1 KB (ATmega328)
Clock Speed 16 MHz
After posting last night I breadboarded 4 or the temp sensors with a resistor and some jumpers, made three connections to the Ardunio and loaded some software from the web and was reading the temp from all four sensors with very little effort. This morning on the train I worked on merging the code for the SHT15 and the 18B20's but I've not had a chance to test the combined code yet.
The next step will be to make a decision about controlling the heaters.
Bob