I am wondering how much I monthly premium would go up in I had a wood burning stove installed.

It will vary from company to company,

1. in some they may not even insure you
2. it will of course have to be installed by code, but some insurance may require even higher codes, you should ask.
3. Also the area you live in, they often look at a specific area and the higher risks where it may be used more than others. A wood stove in Montana is going to be used a lot more than one in south Georgia

Depends on the carrier. If you already have a good homeowner's policy I would contact your agent and ask what if any ramifications this would cause to your present policy. Some companies may drop you as a customer, some may not. Call before you install the stove as you may not like what you hear and the savings may not be to your liking. Also while you are at it, contact several other insurance carriers and see what they would charge you before you install the stove.

The only way to know is to contact an agent who writes multiple companies - and ask.