There are a variety of encryption methods you could use to secure your traffic, and each one has a slightly different power usage, so I'm going to pick a couple of popular choices. The methodology I use to evaluate each method should be applicable to any other ciphers you find and wish to compare.
AES is one of the most popular symmetric-key encryption algorithms (which means you use the same key to encrypt and decrypt). In terms of security, AES is a safe bet:
Best public cryptanalysis
Attacks have been published that are computationally faster than a full brute force attack, though none as of 2013 are computationally feasible.
The paper Biclique Cryptanalysis of the Full AES describes that AES-128 requires 2126.1 operations, AES-192 requires 2189.7 operations, and AES-256 requires 2254.4 operations to break. On a 2.9 GHz processor, assuming each 'operation' is 1 CPU cycle (probably not true), breaking AES-128 would take a very long time. With 10 000 of them running, it will still take nearly forever. So, security isn't a concern here; let's consider the power aspect.
This paper shows (on page 15) that encrypting a block with AES used 351 pJ. I'll compare this a little later after talking about some other common algorithms.
I asked a question about SIMON and SPECK previously, which is worth a read. Where SIMON excels is in situations where you need to encrypt a little bit of data, frequently. The paper I linked earlier states that SIMON 64/96 uses 213 pJ for 64 bits, which is practical when you only need to send 32 bits of payload.
SIMON 64/96 is significantly easier to break than AES though; the paper I linked suggests a 263.9 operations, so our 10 000 CPU setup could crack the encryption in only a few years, as opposed to millions of millennia.
Does it really matter?
At the rate you plan to transmit, the answer is almost certainly no; the energy usage from cryptography will be entirely negligible. For AES, you would use 50 544 pJ per day, so a cheap carbon-zinc AA battery with 2340 J of energy would last far beyond the device's lifetime. If you re-evaluate the calculations with SIMON, you find that it also has a very long lifetime
In short, unless you're transmitting very frequently, the radio is far more of a concern for power. Wikipedia quotes the power usage as between 0.01 and 0.5 W. If you transmit for 1 second at 0.01 W, you've already used more power than AES did over the whole day.
For BLE, though, you're probably fine just relying on the default security; BLE uses AES-CCM by default for link-layer security:
Encryption in Bluetooth with low energy uses AES-CCM cryptography. Like BR/EDR, the LE Controller will
perform the encryption function. This function generates 128-bit encryptedData from a 128-bit key and
128-bit plaintextData using the AES-128-bit block cypher as defined in FIPS-1971.
There is some concern that there are security flaws with BLE's implementation of the link-layer security though; this is not a flaw in AES; rather Bluetooth SIG decided to roll their own key exchange mechanism in 4.0 and 4.1. The issue is now resolved in 4.2 as the Elliptical Curve Hellman-Diffie is now supported.