Mike,
LSB stands for Least Significant Bit. If the Analog to Digital (A/D) converter converts the input votage to a number containing 8-bits, it is called a 8-bit converter. An 8-bit number can have one of 256 possible values. The least significant bit is the bit representing 0 or 1. If the average value was 45 and had a 1 LSB variation, the values would be 44 and 45 or 45 and 46. Looking at the flat part of the middle of your graph (lower trace) I see values of about 86 and 88 degrees but nothing between those values. And all the steps in the waveform are approximately the same size. These are the characteristics which make me think of a discrete sampling issue. Some A/D boards have resolution (or LSB) equivalent to about a millivolt. Some temperature transducers have outputs of about a millivolt per degree.
If your board has an amplifier, try setting it to a higher gain or, equivalently, reduce the voltage range. If the range is +10 to -10 V, change it to +1 to -1 V. That will make the steps much smaller and appear to smooth your data.
Lynn