Will excercise increase the base level of testosterone in men?

Exercising releases endorphins which is why you're feeling good.

At 39 your testosterone will just decrease naturally. Once you get a certain age it drops and you can only replace it through drugs from the doctor

Yes. Working out (hypertrophy) will cause your body to increase testosterone although compound exercises would be better such as squat, bench press, or deadlift. Cardiovascular exercises such as the stationary bike is good for increased blood flow and lower fat in time that will help you with libido (erections)

link Here is an article on Live Strong about squats and how it can raise testoserone level's. Side note: Make sure form is perfect so that you do not hurt yourself and stretch before.

Lifting (heavy) weights, especially leg exercises, can increase your T by 49%. Cardio doesn't do it though.