well why not just

temp=get_temp()
if temps!=prev_temp
{
store number of occurence of the temp
store 8/16 bit coded new temp
n=0
}
else
{
n++;
}

with a nice shutdown method like
store n

and a nice starting method that does
store current_temp
n=0
prev_temp = current_temp

simple log format, low size
depending of characteristic precision or timespan of the same temps you could choose 8 bit

if you like to compress a litle bit more you could always do a memory alloc like that

| 8/16 bit temp | 1 long flag | 7 bit if (!long) /15 bit if (long)|

the principle is extendable to any precision, data type ... remember that the first bit of a float or long float is sign bit so you can use it to store wether it is a float or a long float (i m no HW guru but there are some tricks in my magic bag)

Glances
Benjamin