Yes you can predict future temperatures, based on past temperatures, using adaptive filtering as well.
The optimal linear estimation of a WSS random process from its past values, which is known as linear prediction, is given by a Wiener filter structure where the desired response to be estimated is the current sample of the input (current temparature in your case) and the filter input is the $N$ past samples of the input, (assuming one step forward prediction of order $N$).
The LMS adaptive filtering algorithm simply approaches this optimal Wiener predictor coefficients for WSS signals and for non WSS signals tries to continue to be optimal by tracking it.
This prediction mechanism does not depend on the physical origin of the signals but on their statistical characterisation. As long as your temperature data posses reasonable degree of correlation within it, then the filter will do its best to predict it.