Because only infinite dimensional, unitary representation of $SL(2,F)$ for a local field $F$ can fail to be tempered, if they are spherical. This follows from the classification.

As Asaf points out, looking at the K=SU(2)-invariant vectors will do the job. You will obtain Eisenstein series and cusp forms. There you actually have non-tempered representations besides the trivial representation. There are atmost finitely many. For $\Gamma$ a congruence subgroup of an imaginary quadratic field, it is an important conjecture that there are non (the analogue of the Selberg eigenvalue conjecture).