You probably have a wrong understanding of how volcanism affect an area if you state that
I don't want to include hot springs
For one, if the magmatic chamber is close enough to the surface to affect its temperature, not having any hot spring means you have no underground water at all, and that's pretty unrealistic.
Additionally, having a tropical jungle is not just a matter of temperature, but also of precipitation. Oregon is known for having a rain forest, but it's far from being a tropical region. It "just" gets a lot of rain. Again, availability of water is important.
If you want to achieve what you envision, you probably need to have large hot springs constantly pouring out hot water, which percolates on the ground keeping it warm. The evaporation of the water, condensing as mist on larger area, can keep the whole island moist and with more favorable temperatures than just the geographical location would allow.
Don't forget however that the closer to the poles you get, the longer the nights in winter are. Plants also need light, and without that they are not going to grow. But maybe that can be tweaked with having only yearly plants growing big, with no trees.