Dodging the subject of the Bosch painting, which is certainly a fascinating one, but not directly related to the Templars, there is an important fact about the ancient Templars which is almost universally ignored, which is THEY WERE MONKS.
Shortly after the Order came into being, they came, or brought themselves, to the attention of Bernard of Clairvaux (later St. Bernard), a reforming abbot who was at the time (early 12th century) one of the best known and most influential leaders of the Church. Bernard helped to arrange for the new order to be placed directly under the control of the Pope alone, making them exempt from any control, interference, taxation or payments by any authority, whether civil or ecclesiastical. He also wrote a rule for the Templars. A monastic rule is a set of regulations to be followed to the letter by all members. The Templars thus became an organization of monks and their rule included, as all rules did, the three vows of Poverty, Chastity and Obedience. The vow of Obedience required them to give total, immediate, and unquestioning obedience to their superiors. That of chastity required they be unmarried and live chaste lives. By the vow of poverty they renounced and made over to the Order, at the time of their initiation, any and all property of any kind (even their personal effects) which they then possessed and also gave over to the Order any right they might have in anything they might acquire in the future. The rule required that they attend, if not actually engaged in their military duties, the canonical offices every day. They advanced into battle with the Beauceant and religious banners flying, singing the ancient hymn Vexilla Regis Prodeunt, The Royal Banners Forward Go. Even in the field, they began every day with Matins and Prime and ended every day with Vespers and Compline.
Much has been made of the enormous wealth which the Order accumulated. The most popular explanation is that they discovered a great treasure in the ruins of the Temple in Jerusalem, but there is a much simpler, though less romantic, explanation. Law and custom in Europe at the time stipulated that on the death of a landowner his real estate with all castles, manors and other buildings passed undivided to his eldest surviving son or, in default of a son, to the nearest male heir. This meant that younger sons (cadets) had to be provided for, since they were an expense and maybe a nuisance if they stayed at home. It was customary for cadets to be placed with friendly lords as esquires so they could eventually become knights and support themselves by fighting; a second or third cadet was often given to the Church, the family paying for him to be educated and eventually receive a benefice, or even a bishopric if the family were very rich. The Templars promptly became a respected and popular order, and provided an attractive way to dispose of cadets, and many younger sons of wealthy families became Templars. However, given the mortality of that era, it frequently happened that the elder son or sons died untimely and a cadet became the heir. If that cadet was a Templar, the estate became the property of the Order and was administered by the nearest Temple or by agents hired by them and the estate and its revenue was subject to no taxes or other charges. Over the course of the 12th and 13th centuries, the Order accumulated many such properties over much of Europe, the revenue from which was the basis of the international banking system which they set up and which brought in even more revenue. Ironically, this turned out to be their downfall, since it aroused the greed of Philippe le Bel.
What does this have to do with Masonry? Probably nothing, of course. The Templars in their day had plenty to do without engaging in philosophy or architectural studies, although they had very competent, even brilliant, engineers and builders in their ranks, as is shown by their buildings which have survived. But the pitiful remnant which was dispersed all over Europe after the Dissolution in 1307 was still bound by their vows and the Rule. My own guess was that mostly they sought refuge in monasteries as the only way to fulfill their monastic vows. It is just barely possible that if a significant number escaped to Scotland and managed to form their own community and practice the Rule, they could have helped out at the Battle of Bannockburn, but that is speculation only. The Robinson Theory of how they transmuted themselves and their successors into Free Masons is an attractive one and well thought out, but still unproven.