I can see three possible solutions.
Custom server
It is not the matter of "warming" anything up. Simply - libSVM is the C library, and you need to pack/unpack data into correct format. This process is more efficient on the whole matrices than on each row separately. The only way to overcome this would be to write more efficient wrapper between your production env and the libSVM (you could write a libsvm based server, which would use some kind of shared memory with your service). Unfortunately, this is to custom problem to be solvable by existing implementations.
Batches
Naive approach like buffering the queries is an option (if it is "high performance" system with thousands of queries, you can simply store them in N-element batches, and send them to libSVM in such packs).
Own classification
Lastly - classification using SVM is really simple task. You don't need libSVM to perform classification. Only training is a complex problem. Once you get all the support vectors (SV_i), kernel (K), lagragian multipliers (alpha_i) and intercept term (b), you classify using:
cl(x) = sgn( SUM_i y_i alpha_i K(SV_i, x) + b)
You can code this operation directly in your app, without the need to actualy pack/unpack/send anything to libsvm. This can speed things up by the order of magnitude. Obviously - probability is more complex to retrieve, as it requires the Platt's scaliing, but it is still possible.