Honestly, I didn't think that much about it - they were neutral in the war, so the alternate outcome didn't affect them that much. Most probably they are pretty similar to OTL.
You're welcome to write something about their war/post-war history, as you certainly know the history of the countries better than I do
So your POD is a more aggressive Allies pushing deeper into Eastern Europe? Does this mean a more confident and powerful west vis-a-vis the communists?
Who becomes president in 1948?
Let's see...
The earlier and sharper Cold War is likely to go one of three ways, in descending order of likelihood. The key variable is relations with the Western leaders:
1. Quicker rehabilitation and reduced isolation of Franco as the war against fascism is eclipsed by the anti-communist sentiment. Spain's regime was remarkably free of concrete definition and policies which made it able to adapt to changing geopolitical times. Franco after 1943 was already reorienting the personnel and propaganda of his regime to emphasise "Catholic" and "Western" instead of the more fascist elements (Opus Dei and other catholic technocrats broadly displaced the Falange fascist elements, taking their positions of power over the 50s and 60s), trying to capitalise on anti-communist sentiment and secure the legitimacy and economic assistance he desperately needed.
IRL, Spain was only allowed into the UN in 1955, and didn't join NATO until 1982, post democratisation. It was a pariah state at the end of WW2 for its fascist sympathies, having nearly entered the war on the Axis side, and was deliberately excluded from all major European institutions from Marshall Plan to the Coal and Steel Community to NATO. After the war, Spain basically was cunningly opportunistic, it traded strategic cooperation with the US (there's a huge air force base in Zaragoza, and a US Naval base at the Spanish fleet headquarters at Rota in Cádiz, both established in the 1950s) for reduced isolation. There's scope for them to be able to do this more, and earlier. Maybe the US does something like basing an entire Mediterranean fleet in Cartagena and Rota...
You've got Spain in NATO in your map, you should probably remove them and leave them neutral/non-aligned but cooperating at a grand strategic level. In this timeline, even if democracy wasn't an issue for joining NATO (greater sense of emergency would lead to less European selectivity about friends), I still can't see Spain joining because of its disputes in North Africa and especially with the UK over
Gibraltar. If you're going to have Francoist Spain in NATO in the late 1940s, you're going to have to resolve the Gibraltar dispute because Spain would
never have joined an alliance which meant that it had to consider an attack on Gibraltar an attack on the UK and thus help defend it.
Even given the greater threat in the Mediterranean, there's really not much incentive for NATO to accept a weak, poor, barely industrialised, non-democratic, autarchy-oriented, post-conflict country, especially since in the 40s and 50s it was fighting in Morocco and mostly losing.
Here's a possibility: US need for those bases earlier than in our timeline leads to them pressuring the British to give up Gibraltar as part of a grand three-way pact? Alternatively, there's evidence that Franco would have traded the renunciation of Spanish claims on Gibraltar for enough concessions in the late 40s, I suspect full access to Marshall Aid might have done it.
Another more realistic possibility might be the inclusion of Spain in the Marshall Plan in exchange for these bases leading to earlier and greater economic development and industrialisation with unknown consequences into the 50s, 60s and 70s. Maybe a reinforced Spain is in a better position to retain parts of North Africa like Ifni. That probably depends on what happens to France's colonies, though.
2. The same level of isolation (bases, token aid, but no Marshall aid or access to things like the European Coal and Steel Community/EC) or greater isolation because the formation of a coherent western alliance happens earlier, and Spain's crimes and politics might be less easily forgotten even given the anti-communist mood. Might Eisenhower's successor be a stauncher anti-fascist than the leaders IRL?
There's a possibility that the anti-fascist, pro-democratic resentment against authoritarian Spain results in a formal pact to isolate Spain until it democratises. Perhaps the West has greater confidence than in our time-line, and feels it can afford to keep Spain at arms' length. Not that likely though. The problem with this scenario is the NATO worry would be that there is a communist revolt against Franco and I can't see them doing anything to encourage that.
2.a. A Second Civil War. An intriguing but unlikely sub-branch of this "still isolated" scenario is that a more mischievous Soviet Union with a foot-hold on the Mediterranean starts supplying these partisans and a second Spanish Civil War develops, with the West eventually backing Franco. Spain was pretty fatigued of war by 1944 and civil wars are generally borne from endogenous, nor exogenous causes. however the divisions and resentments were sill there and maybe enough chaos could be sewn to spark another one. Something like the death of Franco at the hands of a partisan bomb, exposing the contradictions in the different factions of the victorious coalition. 19th century Spain was had several politically motivated civil wars and more coups than you've got fingers, the pattern stopped for a while but returned in the 1920s and 1930s (the victory of the Francoist rebellion resulted in the third total reorientation of the Spanish state in 20 years)... why wouldn't the chaotic 150-year pattern continue for longer?
A second civil war would likely render the already impoverished Spain an unstable, conflict-racked third world basket case for decades to come, probably on par with North Africa or Latin America in terms of human development. You can't have an economic miracle with no political stability.
3. Allied liberation of Spain probably isn't likely, but it depends on how you see your Eisenhower replacement's views and thus what happens to American/Allied politics. What happens to the strength of anti-fascist sentiment in the years 1944 to 48 relative to our timeline?
Trends in Italy and elsewhere tell us it'd get forgotten in favour of anti-communist expediency, but what if, as an almost-belligerent, Franco is just seen as too closely tied to the fascists to survive? You've posited a more aggressive west, is the aggression confined to anti-communism or is it anti-fascist too?
One thing to remember is that there were still anti-Franco partisans fighting in Spain in 1944, operating across the border with France. The situation was still fluid, being a time of war. Perhaps someone might convince the Allies to roll in, perhaps Franco's fragile regime falls in short order and Spain gets its own version of Adenauer, a Christian democrat leader who dominates the post-war reconstruction... someone like the pre-war democratic/constitutionalist right leader Gil Robles. Backed up by Marshall aid, NATO membership, and US bases, it would probably lead to a more rapidly industrialising and developing Spain. Hell, even the Costa del Sol might develop earlier... yay.