It is doable.
I would recommend using some cheap RF links like those sold at sparkfun. They can be had cheaper even on ebay.
They may require encoding. I wrote a small library for this, here's a page about it.
I have also made a wireless t/h sensor with bluetooth, here's a writeup about it.
I recommend sensirion sensors for this task. Here's an old writeup about those on arduino.
If you are looking for minimal power consumption, you could use some kind of sleep mode on the MCU. A more efficient way of doing this would be to have the arduino store the readings in local memory. When the memory is full, the data could be sent to home base. The RF transmitter can be switched on/off using a switching transistor so it is powered only when data needs to be sent.
To store more data on the arduino between uploads to home base, I would use a modified version of elias gamma code. This encoding saves space by storing the difference between the last¤t readings.
An extra two bits could be used to represent:
00 - no change
01 - absolute reading - followed by 16-bit integer indicating absolute reference. Used to begin encoding and also when change in reading is more than 15.
10 - positive change
11 - negative change
the last two are needed since gamma code only stores positive integers.
Using this encoding scheme on temperature readings, I have attained 300% compression. Where a day's worth of readings at one per minute, with integer resolution, would consume 2,880 bytes, encoded it may be as small as 1k. So, using this encoding up to a day of readings could be stored on an ATMEGA MCU's limited RAM.
The cost for the transmitter might be-
$6 - atmega8, RBBB
$25 - SHT71 temp/humidity sensor
$10 - TX/RX pair
Receiver- atmega w/ rbbb, $6, using receive module from above. Plus any additional hardware to interface to an LCD display or a PC.
Hope that helps get you started in the right direction. At least, I can say with certainty that you could do at least 3 wireless sensors with a receiver, for $100.
Also note, ne of the battery-operated sensors could run up to 6 months on 4 AA lithium batteries, if you integrate the power saving features I mentioned above.