I should have put this in a different way. You say exersize = stress, but you mean metaphysical stress - not true. What is true is exercise = physical stress which will be beneficial to conditioning your heart.
I actually buy this at all. There is a forgone conclusion in your question: excercise = stress. That's not the case. In competitive sports maybe, but that's not what we are talking about here. The warm up should be done for other reasons namely to get your tendons/muscles used to the stress to come - and I mean "stress" in the physical sense and not related to an Adrenaline rush.
From what I understand, the Heart is being held back all the time at rest. If you unplug your nervous system from the heart it will shoot up to around 100 bpm and that's with no adrenaline. The reason is probably reaction time. If you have a sudden scare, adrenaline surges into the bloodstream but takes a few seconds to really get the heart racing. To make this more efficient, the vagus nerve switches off the brakes, it releases the heart to let it start going fast quickly. This is why you suddenly feel it 'kick' and beat hard/fast. Then the adrenaline surge reaches the receptors on the heart and speeds it up even more. Your digestive system basically shuts down as does urine refinery. All possible blood is put to the brain and muscles for fast thinking (which is why time seems to slow down). When exercising the whole system is far more gradual and not a shock to the system. Research has shown that exercise can reduce anxiety levels and make it more controllable. When you let your heart suddenly jump into overdrive such as with an anxiety attack, there is a higher change of the heart rhythm being corrupted. As flycaster says, a gentle warm up is much better. For example, walking slowly, then brisk walking before getting into a jog. It's just as important to gently slow down at the end of exercise routines, by just walking around for a few minutes to let everything calm down.
Exercise is suggested after a warm-up, sudden boosts of adrenalin are very difficult on the heart. As Ed suggests, what ever is necessary to keep from spiking adrenalin will help, be it slow warm up before exercise, drugs to prevent anxiety, a diet which will lower blood sugar, etc.
to reduce the risk of heart disease through anxiety, you need to keep your blood pressure checked and speak with your Doctor about the possibility of needing some help with councelling or medication.
you think that the heart increases in rate when exercising through fear?
A d are there ways to reduce the risk of Heart problems caused by anxiety?
In that case, why is it that increased heart rate from exercise is considered healthy?
yes, absolutely. The body isn't designed to cope with prolonged episodes of stress on a regular basis. The whole system was put there for fight/flight response so we could fight our enemy or run away. Unfortunately, society is geared around activating this system virtually non-stop.