So is it just hard to engage any gear when hot or is actually hard to move thru the H pattern ?
If its just the engagement trans oil condition could give ya a similar problem but its usually the other way around.... hard to shift when cold.. But low trans oil can give this symptom as the synchro rings wont spin fast enough due to lack of lubrication..
So i would go about it in this order so you dont jump to conclusions,
Check that your gearbox is actually still bolted to the bellhousing and bellhousing bolted to the engine haha..
Check g/b oil level with car level and removing the fill plug on the side oil should be up to this level (usually a bit will come out when ya take the plug out..)
Check oil condtion when ya check the level.. if its been filled with 80w 90 or so it should be coloured like honey, if its been filled with ATF it should be a nice clean red...
What ya dont want to see is metallic colour through it.. So if fluids bad change it and see how it goes, Or top up as necessary if low
If there is no difference you can check your clutch cable adjustment.. But given that its only when its at operating temperature the problem exists I would doubt its your clutch hey more likely to be wear on the synchro rings inside the box which means rebuild
fyi to get a t5 box rebuilt your looking at least around $600-$700 but if ya need any new parts which you probably will do it could be upwards close to $900-$1,000