I would like to compare two groups (cell populations), from two different RNAseq experiments (sets). However, there are no overlapping groups in both experiments available, so an analysis in limma with batch effect (block design) is not possible. Let's say I have populations a, b, and c in experiment 1, and d, and e in experiment 2, and I would like to compare a with d.

Is there another way to compare the two populations in a sound manner? Or is it only possible to make a heatmap? And compare average cpm values?

There is no way to compare groups a and d, either in a DE analysis or via a heatmap or via comparisons of average expression. If there are any batch effects, comparisons across batches of any type will be compromised - this includes informal visual comparisons. The solution? Design a better experiment.

The way to robustly compare different experiments is by gene set tests. For example, compare d vs e using experiment 2. That gives a list of DE genes with associated log-fold-changes, which we might call the d vs e expression signature. Then use a roast gene set test to examine whether the d vs e signature is up-regulated when you compare a vs b and a vs c using experiment 1.

This method works because it depends on comparisons that are made within each individual experiment --- at not stage are conditions compared directly across batches.

I use this technique in many of my own published papers, if you want to have a look for examples.