Welcome ojniemin,
I'm fairly new here too. Since you didn't go into details about heating system, I'll go a couple of different routes.
If your heating system does not have a thermostat and has a wall plug, you might like something like: Powerswitch tail 2 : ID 268 : $25.95 : Adafruit Industries, Unique & fun DIY electronics and kits
If your heating system as a thermostat, it may just need a relay on a pcb to turn it on and off.
For your wireless, I would recommend looking into Synapse Wireless. They sell RF Engines that are similar in price to XBees. The RF Engines allow you to run code on them, or they can simply be used as a serial replacement like the XBee. You could program the RF Engine to read the different temp sensors and control your heating systems. The advantage they provide me is I don't need an Arduino/Xbee combo at every place I have a sensor or control unit.
Synapse site: http://www.synapse-wireless.com/index.php?mainID=3&subID=3&type=product&prodID=3
For 15m, their non-amplified module will probably work:
RF100P86: http://www.futureelectronics.com/en/technologies/semiconductors/wireless-rf/rf-modules-solutions/802154-zigbee/Pages/2270387-RF100P86.aspx
RF100PC6(Amplified): http://www.futureelectronics.com/en/technologies/semiconductors/wireless-rf/rf-modules-solutions/802154-zigbee/Pages/6691737-RF100PC6.aspx
There are plenty on breakout boards and shields for the Xbee. I couldn't find a decently priced breakout board for the RF Engine, so I made some: http://www.jcwoltz.com/2010/10/synapse-breakout-boards-available-for-sale/
As bleedscarlet mentioned, you could do the logging on your computer in the house. It doesn't matter which route you take, it can be done on both.
If you want to take the arduino route, I would recommend not using a mega 2560 for this. You could use an Arduino Prohttp://www.sparkfun.com/commerce/product_info.php?products_id=9219 and then an XBee regulated explorerhttp://www.sparkfun.com/commerce/product_info.php?products_id=9132
Then the datalogging shield you mentioned.
Good luck with you project!