Estimate frequency and peak value of a signal's fundamental
There are a few Matlab implementations of various frequency estimators here.  However, they will probably be "tricked" by the higher harmonics.

That you know a range, perhaps the best technique is one of Eric Jacobsen's estimators. Have a look at his page.

In essence, Eric's estimators use the FFT bin at $X(k)$, and on either side of ($X(k+1), X(k-1)$) the peak.  If you choose your FFT length to match your known range (so that $k \rightarrow 3.45$ and $k+1 \rightarrow 3.50$ and $k-1 \rightarrow 3.4$, then you should be good to go.