1). Radiation:
Certain ores (rare) should be radioactive. Radioactive ores deal damage to the hulls of all ships within a certain radius. This is dependent upon the size of the asteroid, the composition of the radioactive ore and the heat. This is similar to the explosion mechanic. The damage will be negligible, but will mount up over time. The radiation will also be present in the ore. Thus, carrying large quantities of the ore for extended periods, passing near the ore or a ship carrying the ore may cause damage.

To make things easier, there can be radiation proof/reducing ships/add-ons. The thickness and material of the hull will count here. Also, in keeping with science, carrying carbonic ore along with radioactive ore will increase radioactivity, while carrying silicate will reduce radioactivity.

The upsides of this change are:
Use of better/more ships
More realism (I don't know if this is an upside)
Increase in active mining
Player created ore traps: orefields where players drop large quantities of radioactive ore to deal damage to opponents.
I'm sure the players can find many other uses.

The downsides are:
Long range transport of radioactive ores will become difficult.
Super hot radioactive asteroids may deal damage to players far away from it too. This risk is however mitigated by the fact that heating an asteroid to such levels will also be difficult.

2). Heat causes damage:
Similar to radiation, plain heat in any asteroid can also cause damage. This can start when an asteroid is heated beyond 100K. Again, the radius and damage depends on heat, and size.

The upsides are:
It encourages prospecting. Players stop relying on a few select asteroids and overheating them.
It prevents sadistic practices such as heating an asteroid to superhot temperatures to prevent other players from mining (this is actually done, as I'm sure you know).

The downsides are:
I can't think of any.

3). Asteroids heat differently according to composition:
While the heat/cool rate of asteroids and ice crystals does vary based on size, it can also be affected by the composition. For example, a ferric asteroid will heat and cool fast as iron(ferrum) is conductive to heat while a carbonic asteroid will heat and cool slowly as it is an insulator of heat. You can add various conductive/insulative properties to the fictional ores such as Heliocene or Xithricite.

Upsides:
More realistic.

Downsides:
Can't think of any.

4). Cooling beams:
I'm sure this has been a long standing demand. A beam that cools asteroids. I think that making beam that just absorbs heat won't work, because a) it is unscientific and b) it makes it boring.

I suggest making a beam such that it uses a particular ore to cool down the asteroid. Not just to manufacture the beam, but to actually use it. I suggest aquean, as it is both scientifically sound and is also common enough to make it worth it. It also gives some use to aquean ore, which is largely useless otherwise.

Upsides:
It fulfills a long standing demand while not making it too easy.
It provides a weapon against griefing tactics such as overheating asteroids.
Downsides:
Players may use it to infinitely mine an asteroid.

I forgot to write this...

The last change to make it all possible:
Customisable hulls:
Instead of ships having fixed armour, mass and(if this suggestion is added) radiation resistance and heat resistance values, ships can simply be frames or structures, with a fixed volume of hull they can hold. The material of the hull can be chosen from a variety of trade items and other materials. These materials have different stats and prices. They have to be provided by the player.
For eg.
Steel: Heavy, not much armour power, decent radiation resistance and heat conduction. Low price.

Plasteel: Superlight(it's plastic-steel), very low armour, no radiation resistance, low heat conduction. Slightly more expensive.

Lead(new material, which makes all above edits possible): Superheavy, decent armour, the best radiation resistance, heat conduction between plasteel and lead. More expensive, but used only for mining/transporting radioactive material.

Xirite Alloy: Light, Good armour, radiation resistance(unknown), heat conduction (unknown). Expensive

Silksteel

Synthetic Silksteel

All qualities given above are either according to the game description or the real life qualities of existing materials. Proper numerical values can be filled in by more... experienced hands.

A player will be able to buy a given hull only if the material is provided. So, if a player chooses to buy a ship with a Silksteel hull at Odia, they will have to get the Silksteel from Latos, as it is the nearest place where it is sold.

Upsides of this change:
It makes ships much more customisable
It reduces the need for more new ship designs from the devs, as a lot of customisation is done by the players themselves.
It seamlessly enables the radiation and heat changes.
It is more realistic from an RP perspective

Downsides:
It makes ship buying much more complicated
Players may not be able to get their chosen hull material everywhere, and may have to do a bit of hauling.

One more change
Ship heat:
Ships will get hotteror cooler based on the following factors:
Proximity to a star.
Absorption of heat from nearby hot ships or asteroids
Hull material: A metal hull will tend to absorb heat faster, but cool down faster too and have a less adverse reaction to heat
Friction?

The effects of a hot ship will be:
Faster acceleration
Faster Power cell drain
More damage taken.

Upsides:
Its more realistic
It makes it more immersive(atleast for me)
Makes knowledge of ship customisation a necessary skill(this is both an upside and a downside)

Downsides:
It adds a constant worry of ship heat