I think it is a little difficult to define this. Temptations arise through thoughts. But isn't it Satan who suggests bad thoughts?

Satan certainly can suggest bad thoughts, but he's not the only means by which we may receive bad thoughts. For example, if a man sees a pretty scantily dressed woman, the flesh will respond by prompting certain thoughts. The mind knows what is or is not appropriate, the flesh does not. The prompted thought is not sin, but if when the thought gets processed by the mind one does not respond in an appropriate way, then sin occurs.

In the example you gave there is an external influence, but is it a temptation from without?
What could arise from within? I can only think of physical needs - hunger, thirst, the urge for sex, etc. But these are only physical reactions or needs; they don't constitute temptations in themselves. However, Satan takes advantage of them and suggests sinful thoughts.
So, to me, a temptation from within is just a temptation originated from physical needs, and a temptation from without is a temptation not originated from physical needs (for instance, a temptation to lie, to steal, etc.)

Does it require our five senses to be tempted? Or, can we be tempted without them? If so, how?

Tom I find your intentional use of the word “nature” synonymous with “flesh” disturbing. Please do not excuse yourself on ‘countless SDA authors’. I have no contention with them.

I would like you to define your thought as “sinful flesh” and stop using “nature” as a synonym for “flesh” which scripture does not allow.

These are two definitely different meanings and must be kept so. Without this difference you can talk forever to no end and no understanding.

If you are quoting, then please clarify which meaning you think was used.

I hope this will be adopted.

Good point, John. The problem is that even Ellen White uses the terms sinful flesh and sinful nature interchangeably. So, I like your suggestion that we use language that makes clear the difference between sinful character and sinful nature, the difference between the mind of the flesh and the mind of the new man. Also, would you agree that there is essentially no difference between the mind of the flesh and the mind of the old man?

For example, a closer look at the following quote reveal helpful and important insights:

AH 127, 128
The lower passions have their seat in the body and work through it. The words "flesh" or "fleshly" or "carnal lusts" embrace the lower, corrupt nature; the flesh of itself cannot act contrary to the will of God. We are commanded to crucify the flesh, with the affections and lusts. How shall we do it? Shall we inflict pain on the body? No; but put to death the temptation to sin. The corrupt thought is to be expelled. Every thought is to be brought into captivity to Jesus Christ. All animal propensities are to be subjected to the higher powers of the soul. The love of God must reign supreme; Christ must occupy an undivided throne. Our bodies are to be regarded as His purchased possession. The members of the body are to become the instruments of righteousness. {AH 127.2}

In this passage she says the terms flesh, fleshly, carnal lusts, animal propensities, and the lower, corrupt nature are synonymous. She also says it is the seat of our lower passions, the source of temptation, and the origin of our sinful thoughts and feelings. In other words, our sinful nature has, as it were, a mind and voice of its own.

But she also makes it clear that our sinful nature cannot act contrary to the will of God. It can generate and communicate sinful thoughts and feelings (i.e., temptations), but it cannot commit a sin. However, in the mind of the old man, we cannot resist them, so we end up desiring them or doing them, thus we become guilty of them. As such there really isn't a whole lot of difference between the sinful character we develop as a result of naturally acting out the lusts of the flesh and sinful nature itself. In fact, it could be accurately stated that sinful character is nothing more than sinful nature manifested, or personified. "Now the works of the flesh are manifest, which are these..." Gal 5:19.

But, in the mind of the new man, we may recognize the unholy thoughts and feelings produced by our sinful nature and, by the indwelling grace of God, resist them unto the honor and glory of God. In this regard Jesus is our example. "Those who overcome will follow the example of Christ by bringing bodily appetites and passions under the control of enlightened conscience and reason.” CON 74.

TE 146
Man, through yielding to Satan's temptations to indulge intemperance, brings the higher faculties in subjection to the animal appetites and passions, and when these gain the ascendancy, man, who was created a little lower than the angels, with faculties susceptible of the highest cultivation, surrenders to the control of Satan. And he gains easy access to those who are in bondage to appetite. Through intemperance, some sacrifice one half, and others two thirds, of their physical, mental, and moral powers, and become playthings for the enemy. {Te 146.1}

Those who would have clear minds to discern Satan's devices, must have their physical appetites under the control of reason and conscience. The moral and vigorous action of the higher powers of the mind are essential to the perfection of Christian character, and the strength or the weakness of the mind has very much to do with our usefulness in this world, and with our final salvation. {Te 146.2}

3T 84
The unsanctified will and passions must be crucified. This may be regarded as a close and severe work. Yet it must be done, or you will hear the terrible sentence from the mouth of Jesus: "Depart." You can do all things through Christ, who strengtheneth you. You are of that age when the will, the appetite, and the passions clamor for indulgence. God has implanted these in your nature for high and holy purposes. It is not necessary that they should become a curse to you by being debased. They will become this only when you refuse to submit to the control of reason and conscience. {3T 84.1}

In other words:

The mind of the flesh is the physical genetic inheritance as well as physical cultivated habits.

The mind of the old man is a result of the “heart-spirit” aspect of chosen, educated and practiced thought, values (or lack of) and principles (or lack of).

I'm not totally sure, but it sounds like we both agree on the differences between flesh (nature) and spirit (mind). The mind of our old man (our cultivated sinful traits of character) is the personification (manifestation) of the mind of our sinful flesh nature (our inherited sinful traits of character). It sounds like you also make a distinction between cultivated and inherited sinful traits of character. That is, we possess way more inherited traits than we can possibly cultivate in our short lifetime and, therefore, do not manifest themselves, thus we are not guilty of them. Is that how you see things?