Maybe if muscles hur. Work with a good physical therapist. Find musculoskeletal acupuncture such as trigger points (don't need injections, just 'dry needling'). A good hands-on osteopathic physician who does omt (omm) is key for maintaining function in a chronic situation. Finally since this is really arthritis in the spine, and has an inflammatory component, eat an anti-inflammatory diet and herbs (find online).
Possible. Sometimes there can be muscular symptoms related to spinal stenosis that heat application may help with but will not affect the spnal stenosis itself.