The fact that he could not be warmed by artificial means (specifically clothes) is explained in Rashi on I Melachim 1:1
But he was not warmed: Our Rabbis concluded and said: “He who disgraces clothing will ultimately be deprived of their pleasures.
Because David tore the skirt of Saul’s robe (Samuel I 24:5)
consequently, they did not warm him” (Berachoth 62b). As David saw the
angel of death standing in Jerusalem and his sword in his hand, his
blood became cold from fear of him.
Just as clothing would not help, a fire would not help either. A fire would have had to be kept going constantly and would just make the room hot without helping the king. A hot bath would be temporary even if it would work.
Rashi on I Melachim 1:2
A virgin: her virginity warms her flesh.
A warmer: Heb. סכנת a warmer, and similarly “and he who chops wood is warmed (יסכן) by them” (Eccl. 10:9).
explains that his wives could not help because they were no longer virgins. This means that the medical advice of that time was that he required the extra warmth provided by her virginity. It does not matter as to whether or not we treat it as medical fact or speculation. The JPS translation of I Melachim uses Rashi to say
- A virgin - Since his own body was not capable of producing its own warmth in sufficient amounts, an alternative was sought to aid him
in this capacity. His medical advisers felt a woman could accomplish
this best. Although he had eighteen wives for this purpose, yet none
had the advantages of a virgin, since her virginity warms her flesh.
Her vibrant youth and virgin blood increased the warmth of her flesh.
[Rashi]
The significance of this story is that Adoniyahu was actually setting up a revolt against Shlomo Hamelech. as we see in I Melachim 2:17 in the JPS commentary
17 ... that he give me Abishag the Shunamite as a wife - Herein
Adoniahu discloses the true purpose for the lengthy introduction. His
motive in seeking to marry Abishag was not an expression of his love,
but rather a means of justifying his claims to the throne. Since all
of a king's possessions are prohibited for use by a commoner, after
the king's death, then certainly Abishag, who was in the same category
as a wife, his most personal possession, should not be available to
Adoniahu, a commoner. The only exception to this prohibition would
be the next king. If Solomon would grant him permission to marry
Abishag, his claim to the throne would be greatly enhanced. Adoniahu,
therefore, sought to conceal his true intentions by renouncing his own
claims to the throne and acceding to and granting Solomon's
[Abarbanel]
Shlomo Hamelech understood what was going on and as we see in I Melachim 2:22
- And king Solomon answered and said to his mother, "And why do you ask
Abishag the Shunemitess for Adoniahu? Ask for him the kingdom
(also), for he is my elder brother, and to him, and Abiathar the
priest, and Joab the son of Zeruiah."
Rashi
… ask for him the kingdom also: From the moment a commoner uses
the scepter of the king, that is the beginning of authority.
As the JPS explains
… ask for him the kingdom also: Solomon grasped immediatel the implications of this request. Adoniahu had no more desire to marry Abishag than he had. Solomon understood his intentions to use Abishag as a stepping stone to the throne. Solomon knew from the moment a commoner uses the scepter, or any personal property, of the king, that is the beginning of authority and sovereignty [Rashi]
This cause Shlomo Hamelech to order Adoniahu's death as a mored bemalchus
Malbim explains on I Melachim 2:23
וישבע המלך וכו׳ כי בנפשו דבר – רצה לומר הלא דבר זה דבר במסירת נפשו, כי
בודאי הבין שיש לו סכנה בשאלה זאת, ובשביל נשואי אבישג לא היה מוסר נפשו
אם לא בשחושב תחבולות שבזה שישתמש בשרביטו של מלך יוכל למרוד.
As the JPS explains Malbim
This request is going to cost him his life. Solomon was convinced that
Adoniahu would never endanger his life just to marry Abishag. Most
likely he had other designs in mind, such as making use of the king's
scepter as a beginning of sovereignty*. [Malbim]
JPS cites Abarbanel on I Melachim 2:25 that
Solomon forgave Adoniahu only on the condition that he would not
return to his quarrelsome and rebellious ways. Even the
slightest suggestion of rebellion would rescind the previously granted
pardon. His request for Abishag therefore revived again his earlier
offense in David's lifetime. [Abarbanel]