To "cure" heat, you would have to completely rewrite BattleTech entirely from the ground up. Firstly, the immediate problem is that it would that require you to essentially re-write all the lore, which has that conceit built-in, or if you (onl" introsuce it in the post IllClan timeline, you obivate everything before that future date when you decide heat has been "fixed" (which amounts to the same thing).
But let's ignore that massive gaping problem for a moment and just look at the mechanical situation.
Every BattleMech would have to be re-designed.
Without the check of heat, all mechs would tend towards max armour and the optimum energy weapons; expect to see much more emphasis to go the Blackhawk/ Swayback route or the much-maligned Hellstar route. (As both mechanically and in terms of in-universe logic, otherwise is deliberately nerfing yourself and militaries aren't that stupid that consistently); without the limitations of heat, LRMs would be literally the only ammunition dependant weapon that would be worth producing, only because they are capable of engageing outside direct-of-sight. The guass rifle would be instantly obsolete, as you can mount two ER PPCs for less tonnage and space (on either tech base). Even AC 20s, too; why bother with 5 extra damage to one location, when for less tonnage and far less space you can have +50% damage overall? And even heavy Guass Rifles get replaced by three ER PPCs instead.
The Hellstar, from being the best heat-neutral ER PPC platform, would be A Good Starting Point. (Take off twenty double heat sinks, that's another three ER PPCs right there...)
So, what do you do instead? You could say "vehicles are heat-neutral, so that's fine..." Except they aren't. Vehicles are explictly REQUIRED to mount enough heatsinks to be heat neutral (or have power amplifiers or both, I forget which), solely because the conciet of the game was to have them in a supporting role and thus explictly NOT to have the added complexity of them having a heatscale too. (There's no earthly reason aside from that why vehicles couldn't be given a heatscale and that option. Hell, at one point, I literally made some house rules to that effect that to mechanically treat them as equals, which was extensive as simply the effort to kludge-up record sheets in the mid-90s without a computer, armed only with photocopies, scissors, tipex and pritt-stick...)
But if you implemented that, it begs the question of why not just use the already-existing heat-neutral mechs or make your own variants for when you are introducing new players or when playing yourself. (I mean, for that matter, literally the first thing I did after getting my boxed set was start making my own Clan homebrew mechs (parts then played by LEGO spacemen) deilberately alpha-capable...) That is by far the easiest solution to the stated problem of the presumably localised problem of "I have new players that can't manage the heat system." (Since a lot of new players coming to the game will be coming from the computer games and I assume are expecting heat management...)
Okay, so that solution is probably not worth doing, then; what if instead you say "well, instead you make power plants produce an energy rating and make energy weapons have a power draw as a balance instead." But... How it that different from the heat system, fundementally?
By the time you have answered the question of "but what if I want to turn these guns off to shoot these other guns" and "but what happens when I try to plug everything in at once anyway" and have replaced the heat scale with the "power drain" scale when the powercore shuts down because you pushed it too hard rather than overheated, you will have gotten back 90% of the heat system anyway at the loss of some of the unique BattleTech flavor anyway.
And there's the rub. If you take away heat management, you have lost some of the critical flavour for BattleTech - as both a fictional universe AND as a set of rules. You would have Age-of-Sigmar'd BattleTech's fanbase and, if the recent survey is any inidication, tweaked off a significant portion of the fanbase.
(Let's be real - CGL is never going to even look in the direction of these solutions anyway, for the obvious reasons. Heat is here to stay in BattleTech, whether or not any particular player's feeling towards it.)
I'll be honest, though, I feel like taking away the heat management aspect from BattleTech is like taking the critical hit table away from Rolemaster; it's a not insignificant part of why you play the rules in the first place. BattleTech as a set of rules sits in an odd position. The base rules are rather dated (flip-side - they also haven't changed significantly in 40 years). The heat system adds another, is fairly small, tactical decison making level, but one that is, to my knowledge, pretty unique. (But if someone doesn't find that compelling personally, that's fine; not every set of rules has to cater to everyone.) The supplementary rules material makes BT much more fleshed-out than most other wargames rules and considers a lot of aspects that other rules don't, like dead ground (which to my knowledge, I can only think of Maneouvre Group which also considers that); but those are exactly the sort of rules you WON'T be using with new players, which was one of the conceits for getting rid of heat.
So by the time you have stripped away the heat management system (making a system which has less interesting decisions to make, and decisions, not dice-rolls, are what makes a good set of rules) and are ignoring the ancillary areas, you are left with a fairly mediocre set of rules which is out-performed by newer sets of rules. And what you have left is not really BattleTech.
If it not for the flavour I wouldn't play BattleTech myself (and in fact, when I'm not using my mechs I don't; hell, even when I do play BT, I've butchered a lot of the base engine rules with pasted-on bits of Maneouvre Group, as no set of rules has ever survived contact with me without moderate to extreme houserules).
So one might beg the question, at that point, as to whether it would not be better to just use a different set of rules to start with for those toys, rather than try removing a fundemental core aspects of the BattleTech rules and trying to fill-in the cracks. (As not even GW have yet managed the feat of sending people round your house to punish you for using their figures in not the proscribed fashion, though they do seem to be working up to it.) I couldn't personally recommend any sets of mecha-orientated rules from the recent time, I'm afraid (hybridisation aside, regular Sci-Fi Maneouvre Group is definitiely NOT that as walkers tend to suffer from being too tall at half the relative size of BattleMechs!). I presume One Page Rules may have something, I suppose, but I am afraid I am definitively put off by any set of rules which claims to be that short.
(To be precisely clear, this last paragraph is absolutely not me saying "Garagegamer go play some other game," I'm just trying to follow the logicial ramifications of removing heat from BattleTech, I'm trying to get at that at the point the theorhetical person has changed BattleTech from being BattleTech, they might as well have changed to a not-BattleTech set of rules. I mean, if someone really hated the heat system that much it was a deal-breaker for them, that would be an option, certainly, but I didn't get that impression from the OP.)
