Conservation of gravitational thermodynamics

Ok, so most of the heat generated in most planets comes from the radioactive decay of long lives isotopes, with some generated by friction and other sources.

If time passes and the planet "dies" or more simply is put into an isolated state (no rotation, no radiation etc..) so that only gravity is generating heat and any effects created by gravitational forces on the planet (like friction of heated substances and any other compression heat)

Would the amount of heat being generated by the gravitational forces and subsequent reactions and effects create any 'usable' amount of energy. Conservation of energy says no. But how would the math on this work out?

(1)What would be the highest heat/energy 'output' to gravitational 'pull' ratio achievable?

(2)Is there a potentially natural or artificial structure that could increase this ratio? (such as a denser than normal 'crust' less dense 'mantle' etc..)

(3)What does the model of such a planet look like? (is there even a 'core', 'mantle' and 'crust' zones?)

Thanks for any light shed on this 'dark' subject. I've always been interested in this question. Hoping for an answer that will be conducive to scifi writing. Otherwise I'll need to stretch the suspension of disbelief farther than I'd like :)

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
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`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$